Journal of Geometry and Physics最新文献

{"title":"Mirror partner for a Klein quartic polynomial","authors":"Alexey Basalaev","doi":"10.1016/j.geomphys.2025.105538","DOIUrl":"10.1016/j.geomphys.2025.105538","url":null,"abstract":"<div><div>The results of A. Chiodo, Y. Ruan and M. Krawitz associate the mirror partner Calabi–Yau variety <em>X</em> to a Landau–Ginzburg orbifold <span><math><mo>(</mo><mi>f</mi><mo>,</mo><mi>G</mi><mo>)</mo></math></span> if <em>f</em> is an invertible polynomial satisfying Calabi–Yau condition and the group <em>G</em> is a diagonal symmetry group of <em>f</em>. In this paper we investigate the Landau–Ginzburg orbifolds with a Klein quartic polynomial <span><math><mi>f</mi><mo>=</mo><msubsup><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></msubsup><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>+</mo><msubsup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></msubsup><msub><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>+</mo><msubsup><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow><mrow><mn>3</mn></mrow></msubsup><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <em>G</em> being all possible subgroups of <span><math><mrow><mi>GL</mi></mrow><mo>(</mo><mn>3</mn><mo>,</mo><mi>C</mi><mo>)</mo></math></span>, preserving the polynomial <em>f</em> and also the pairing in its Jacobian algebra. In particular, <em>G</em> is not necessarily abelian or diagonal. The zero–set of polynomial <em>f</em>, called Klein quartic, is a genus 3 smooth compact Riemann surface. We show that its mirror Landau–Ginzburg orbifold is <span><math><mo>(</mo><mi>f</mi><mo>,</mo><mi>G</mi><mo>)</mo></math></span> with <em>G</em> being a <span><math><mi>Z</mi><mo>/</mo><mn>2</mn><mi>Z</mi></math></span>–extension of a Klein four–group.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"215 ","pages":"Article 105538"},"PeriodicalIF":1.6,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144139205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Integrable geometric evolution equations through a deformed Heisenberg spin equation","authors":"Dae Won Yoon ,&nbsp;Zühal Küçükarslan Yüzbaşı","doi":"10.1016/j.geomphys.2025.105534","DOIUrl":"10.1016/j.geomphys.2025.105534","url":null,"abstract":"<div><div>Using the geometrical equivalence methods, we showed a deformed Heisenberg spin chain equation is geometrically equivalent to a generalized nonlinear Schrödinger equation. After that, we demonstrate in Euclidean 3-space that assigning spin vectors to the tangent, normal, and binormal vectors of the three distinct moving space curves, respectively, results in the creation of three distinct surfaces. Then we find the Gauss and the mean curvatures of these surfaces, respectively.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"214 ","pages":"Article 105534"},"PeriodicalIF":1.6,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144115946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Moduli spaces of weighted pointed stable curves and toric topology of Grassmann manifolds","authors":"Victor M. Buchstaber ,&nbsp;Svjetlana Terzić","doi":"10.1016/j.geomphys.2025.105533","DOIUrl":"10.1016/j.geomphys.2025.105533","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In this paper we establish fundamental relations between the famous problem of compactifications of the moduli space &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; of ordered &lt;em&gt;n&lt;/em&gt; distinct points on &lt;span&gt;&lt;math&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; and toric topology of the complex Grassmann manifolds &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. The best known is the Deligne-Mumford compactification &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;‾&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. The Losev-Manin compactification &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;¯&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is also closely related to important questions in mathematical physics and toric geometry. These compactifications belong to the family of Hassett compactifications &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;‾&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; of moduli spaces of weighted pointed stable curves. In this paper we show that the orbit space &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; of complex Grassmann manifolds &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; by the canonical action of the compact torus &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; of the complexity &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; serves as a universal space in a sense that for any Hassett compactification &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;‾&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; there exists a subspace &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; in &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; and birational morphism &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;‾&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. We describe large class of the set of weights &lt;span&gt;&lt;math&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; for which this birational morphism gives rise to an isomorphism. This provides topological model for the Hassett category in which Deligne-Mumford compactification &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"215 ","pages":"Article 105533"},"PeriodicalIF":1.6,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144139204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Spectral forms and de-Rham Hodge operator","authors":"Jian Wang ,&nbsp;Yong Wang ,&nbsp;Mingyu Liu","doi":"10.1016/j.geomphys.2025.105535","DOIUrl":"10.1016/j.geomphys.2025.105535","url":null,"abstract":"<div><div>Motivated by the trilinear functional of differential one-forms, spectral triple and spectral torsion for the Hodge-Dirac operator, we introduce a multilinear functional of differential one-forms for a finitely summable regular spectral triple with a noncommutative residue, which generalize the spectral torsion defined by Dabrowski-Sitarz-Zalecki. The main results of this paper recover two forms, torsion of the linear connection and four forms by the noncommutative residue and perturbed de-Rham Hodge operators, and provide an explicit computation of generalized spectral forms associated with the perturbed de-Rham Hodge Dirac triple.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"214 ","pages":"Article 105535"},"PeriodicalIF":1.6,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144115945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fiber bundle structure in Ashtekar-Barbero-Immirzi formulation of General Relativity","authors":"Matteo Bruno","doi":"10.1016/j.geomphys.2025.105537","DOIUrl":"10.1016/j.geomphys.2025.105537","url":null,"abstract":"<div><div>We aim to provide a rigorous geometric framework for the Ashtekar-Barbero-Immirzi formulation of General Relativity. As the starting point of this formulation consists in recasting General Relativity as an <span><math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo></math></span> gauge theory, it naturally lends itself to interpretation within the theory of principal bundles. The foundation of our framework is the spin structure, which connects the principal <span><math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo></math></span>-bundle construction with the Riemannian framework. The existence of the spin structure enlightens the geometric properties of the Ashtekar-Barbero-Immirzi-Sen connection and the topological characteristics of the manifold. Within this framework, we are able to express the constraints of the physical theory in a coordinate-free way, using vector-valued forms that acquire a clear geometric interpretation.</div><div>Using these geometric concepts, we analyze the phase space of the theory and discuss the implementation of symmetries through the automorphism group of the principal <span><math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo></math></span>-bundle. In particular, we demonstrate that the description of the kinematical constraints as vector-valued forms provides a natural implementation as momentum maps for the automorphism group action.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"214 ","pages":"Article 105537"},"PeriodicalIF":1.6,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144115944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On (co-)morphisms of n-Lie-Rinehart algebras with applications to Nambu-Poisson manifolds","authors":"Yanhui Bi ,&nbsp;Zhixiong Chen ,&nbsp;Tao Zhang","doi":"10.1016/j.geomphys.2025.105536","DOIUrl":"10.1016/j.geomphys.2025.105536","url":null,"abstract":"<div><div>In this paper, we give a unified description of morphisms and comorphisms of <em>n</em>-Lie-Rinehart algebras. We show that these morphisms and comorphisms can be regarded as two subalgebras of the <em>ψ</em>-sum of <em>n</em>-Lie-Rinehart algebras. We also provide similar descriptions for morphisms and comorphisms of <em>n</em>-Lie algebroids. It is proved that the category of vector bundles with Nambu-Poisson structures and the category of their dual bundles with <em>n</em>-Lie algebroid structures are equivalent to each other.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"214 ","pages":"Article 105536"},"PeriodicalIF":1.6,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144106558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Non-abelian cohomology of Lie H-pseudoalgebras and inducibility of automorphisms","authors":"Apurba Das","doi":"10.1016/j.geomphys.2025.105532","DOIUrl":"10.1016/j.geomphys.2025.105532","url":null,"abstract":"<div><div>In this paper, we classify the equivalence classes of non-abelian extensions of a Lie <em>H</em>-pseudoalgebra <em>L</em> by another Lie <em>H</em>-pseudoalgebra <em>M</em> in terms of the non-abelian cohomology group <span><math><msubsup><mrow><mi>H</mi></mrow><mrow><mi>n</mi><mi>a</mi><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>(</mo><mi>L</mi><mo>,</mo><mi>M</mi><mo>)</mo></math></span>. We also show that the group <span><math><msubsup><mrow><mi>H</mi></mrow><mrow><mi>n</mi><mi>a</mi><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>(</mo><mi>L</mi><mo>,</mo><mi>M</mi><mo>)</mo></math></span> can be realized as the Deligne groupoid of a suitable differential graded Lie algebra. Finally, we consider the inducibility of a pair of Lie <em>H</em>-pseudoalgebra automorphisms in a given non-abelian extension. We show that the corresponding obstruction can be realized as the image of a suitable Wells map in the context.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"214 ","pages":"Article 105532"},"PeriodicalIF":1.6,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144070481","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bondi-spherically symmetric Einstein-non-linear scalar field system","authors":"Franck Modeste Teyang ,&nbsp;Pierre Noundjeu ,&nbsp;David Tegankong","doi":"10.1016/j.geomphys.2025.105529","DOIUrl":"10.1016/j.geomphys.2025.105529","url":null,"abstract":"<div><div>The study of Einstein's equations coupled with a nonlinear scalar field and a positive cosmological constant provides deeper insight into the physics of the large-scale universe. It also serves as a means to test theoretical models against cosmological observations. In this paper, we consider a characteristic initial value problem defined on a future isotropic cone for Einstein's equations coupled with a nonlinear scalar field and a positive cosmological constant in a Bondi-spherically symmetric spacetime. We establish that, for small initial data, this system possesses a unique global solution in Bondi time, which is causally complete in the future. Additionally, we prove that this solution decays exponentially over time and approaches the de Sitter solution. Consequently, our results provide a nonlinear stability result for de Sitter spacetime within the considered class of solutions, and they also support the cosmic no-hair conjecture.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"214 ","pages":"Article 105529"},"PeriodicalIF":1.6,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144068470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Non-existence of extremal Sasaki metrics and the Berglund-Hübsch transpose","authors":"Jaime Cuadros Valle ,&nbsp;Ralph R. Gomez ,&nbsp;Joe Lope Vicente","doi":"10.1016/j.geomphys.2025.105531","DOIUrl":"10.1016/j.geomphys.2025.105531","url":null,"abstract":"<div><div>We use the Berglund-Hübsch transpose rule from classical mirror symmetry in the context of Sasakian geometry <span><span>[11]</span></span> and results on relative K-stability in the Sasaki setting developed by Boyer and van Coevering in <span><span>[6]</span></span> to exhibit examples of Sasaki manifolds with big Sasaki cones that have no extremal Sasaki metrics at all. Previously, examples with this feature were produced in <span><span>[6]</span></span> for Brieskorn-Pham polynomials or their deformations. Our examples are based on the more general framework of invertible polynomials. In particular, we construct families of links that preserve the emptiness of the extremal Sasaki-Reeb cone via the Berglund-Hübsch rule: if the link does not admit extremal Sasaki metrics then its Berglund-Hübsch dual preserves this property and moreover this dual admits a representative in its local moduli with a larger Sasaki-Reeb cone which remains obstructed to admitting extremal Sasaki metrics. Some of the examples exhibited here have the homotopy type of a sphere or are rational homology spheres.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"214 ","pages":"Article 105531"},"PeriodicalIF":1.6,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144084285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"New weighted Alexandrov-Fenchel type inequalities for hypersurfaces in hyperbolic space","authors":"Peng Pan,&nbsp;Jiancheng Liu","doi":"10.1016/j.geomphys.2025.105528","DOIUrl":"10.1016/j.geomphys.2025.105528","url":null,"abstract":"<div><div>In this paper, we obtain two monotonic quantities under the locally constrained inverse curvature flow. Using the monotonicity, a family of new weighted geometric inequalities for closed static-convex hypersurface in hyperbolic space <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></math></span> is obtained, which implies that, among all closed static-convex hypersurfaces with fixed weighted <em>k</em>-th (<span><math><mi>k</mi><mo>⩾</mo><mn>2</mn></math></span>) mean curvature integral, the geodesic ball reaches the maximum value of <em>l</em>-th (<span><math><mi>l</mi><mo>⩽</mo><mi>k</mi></math></span>) quermassintegral. We also consider the case of <span><math><mi>k</mi><mo>=</mo><mn>1</mn></math></span> and obtain a geometric inequality which is an improved version of Wei and Zhou's result in Wei and Zhou (2023) <span><span>[24]</span></span>.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"214 ","pages":"Article 105528"},"PeriodicalIF":1.6,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144084287","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}