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Annals of Global Analysis and Geometry最新文献

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Conformal actions on the sphere with an open orbit 开轨道球面上的共形作用
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2026-03-17 DOI: 10.1007/s10455-026-10030-x
P. Ahmadi, M. Ahmadifard
{"title":"Conformal actions on the sphere with an open orbit","authors":"P. Ahmadi,&nbsp;M. Ahmadifard","doi":"10.1007/s10455-026-10030-x","DOIUrl":"10.1007/s10455-026-10030-x","url":null,"abstract":"<div><p>In this paper, we study conformal actions on the Euclidean sphere <span>(mathbb {S}^{n})</span>, focusing on the case where the action induces an open orbit. Under this condition, we determine the Lie algebras of the acting Lie groups up to conjugacy within the orthogonal group <i>O</i>(<i>n</i>, 1). Furthermore, we classify these actions up to orbit equivalence and specify the resulting orbits up to conformal equivalence.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147559311","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}
引用次数: 0
Dynamics of Fuchsian meromorphic connections with real periods 具有实周期的Fuchsian亚纯连接的动力学
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2026-03-14 DOI: 10.1007/s10455-026-10033-8
Marco Abate, Karim Rakhimov
{"title":"Dynamics of Fuchsian meromorphic connections with real periods","authors":"Marco Abate,&nbsp;Karim Rakhimov","doi":"10.1007/s10455-026-10033-8","DOIUrl":"10.1007/s10455-026-10033-8","url":null,"abstract":"<div><p>In this paper, we study the dynamics of geodesics of Fuchsian meromorphic connections with real periods, giving a precise characterization of the possible <span>(omega )</span>-limit sets of simple geodesics in this case. The main tools are the study of the singular flat metric associated to the meromorphic connection, an explicit description of the geodesics nearby a Fuchsian pole with real residue larger than <span>(-1)</span> and a generalization to our case of the classical Teichmüller lemma for quadratic differentials.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441927","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}
引用次数: 0
On the variety of Lie algebras endowed with complex structures: degenerations and deformations. 具有复杂结构的李代数的多样性：退化和变形。
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2026-03-13 DOI: 10.1007/s10455-026-10034-7
Edison Alberto Fernández-Culma, Nadina Rojas
{"title":"On the variety of Lie algebras endowed with complex structures: degenerations and deformations.","authors":"Edison Alberto Fernández-Culma,&nbsp;Nadina Rojas","doi":"10.1007/s10455-026-10034-7","DOIUrl":"10.1007/s10455-026-10034-7","url":null,"abstract":"<div><p>We study the space of Lie algebras equipped with left-invariant complex structures, <span>( mathcal {L}_{ J_{tiny {text{ cn }}} }(mathbb {R}^{2n}) )</span>, with particular attention to their degenerations and deformations. To this end, we identify certain invariants that remain well-behaved under degenerations while preserving the complex structure. These concepts are then applied to the four-dimensional case. Additionally, we explore applications to the study of left-invariant Hermitian structures on Lie groups, and we discuss some aspects of the deformation theory within <span>( mathcal {L}_{ J_{tiny {text{ cn }}} }(mathbb {R}^{2n}) )</span>.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441535","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}
引用次数: 0
Weak limits of the J-flow and the deformed Hermitian-Yang-Mills flow on Kähler surfaces: boundary cases Kähler表面上j流和变形Hermitian-Yang-Mills流的弱极限：边界情况
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2026-03-12 DOI: 10.1007/s10455-026-10032-9
Rei Murakami
{"title":"Weak limits of the J-flow and the deformed Hermitian-Yang-Mills flow on Kähler surfaces: boundary cases","authors":"Rei Murakami","doi":"10.1007/s10455-026-10032-9","DOIUrl":"10.1007/s10455-026-10032-9","url":null,"abstract":"<div><p>We prove that if a pair of Kähler classes is <i>J</i>-nef, the <i>J</i>-flow on a compact Kähler surface converges to a weak solution of the Monge-Ampère equation in the sense of currents. We also establish the same convergence behavior for the deformed Hermitian-Yang-Mills flow. The method is based on a property of a limit of viscosity subsolutions.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-026-10032-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Positive Hermitian curvature flow on 2-step nilpotent Lie groups 两步幂零李群上的正厄米曲率流
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2026-03-09 DOI: 10.1007/s10455-026-10031-w
Ettore Lo Giudice
{"title":"Positive Hermitian curvature flow on 2-step nilpotent Lie groups","authors":"Ettore Lo Giudice","doi":"10.1007/s10455-026-10031-w","DOIUrl":"10.1007/s10455-026-10031-w","url":null,"abstract":"<div><p>We study the positive Hermitian curvature flow for left-invariant metrics on 2-step nilpotent Lie groups <i>G</i> with a left-invariant complex structure <i>J</i>. We describe the long-time behavior of the flow under the assumption that <span>(J[mathfrak {g}, mathfrak {g}])</span> is contained in the center of <span>(mathfrak {g})</span>. We show that under our assumption the flow <span>(g_{t})</span> exists for all positive <i>t</i> and <span>((G,(1+t)^{-1}g_{t}))</span> converges, in the Cheeger-Gromov topology, to a 2-step nilpotent Lie group with a non flat semi-algebraic soliton. Moreover, we prove that, in our class of Lie groups, there exists at most one semi-algebraic soliton solution, up to homothety. Similar results were proved by M. Pujia and J. Stanfield for nilpotent complex Lie groups [21, 24]. In the last part of the paper we study the Hermitian curvature flow for the same class of Lie groups.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-026-10031-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147440982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hyperkähler ambient metrics associated with twistor CR manifolds Hyperkähler与扭或CR流形相关的环境指标
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2026-02-12 DOI: 10.1007/s10455-026-10027-6
TAIJI MARUGAME
{"title":"Hyperkähler ambient metrics associated with twistor CR manifolds","authors":"TAIJI MARUGAME","doi":"10.1007/s10455-026-10027-6","DOIUrl":"10.1007/s10455-026-10027-6","url":null,"abstract":"<div><p>Twistor CR manifolds, introduced by LeBrun, are Lorentzian (neutral) CR 5-manifolds defined as <span>(mathbb {P}^1)</span>-bundles over 3-dimensional conformal manifolds. In this paper, we embed a real analytic twistor CR manifold into the twistor space of the anti self-dual Poincaré-Einstein metric whose conformal infinity is the base conformal 3-manifold, and construct the associated Fefferman ambient metric as a neutral hyperkähler metric on the spinor bundle with the zero section removed. We also describe the structure of the Cheng–Yau type Kähler-Einstein metric which has the twistor CR manifold as the boundary at infinity.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147339057","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}
引用次数: 0
The submanifold compatibility equations in magnetic geometry 磁几何中的子流形相容方程
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2026-02-04 DOI: 10.1007/s10455-026-10026-7
Ivo Terek
{"title":"The submanifold compatibility equations in magnetic geometry","authors":"Ivo Terek","doi":"10.1007/s10455-026-10026-7","DOIUrl":"10.1007/s10455-026-10026-7","url":null,"abstract":"<div><p>With the notions of magnetic curvature and magnetic second fundamental form recently introduced by Assenza and Albers–Benedetti–Maier, respectively, we establish analogues of the Gauss, Ricci, and Codazzi–Mainardi compatibility equations from submanifold theory in the magnetic setting.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-026-10026-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147336889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
(F_4) and desmic quartic surfaces (F_4) 以及大地四次曲面
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2026-02-02 DOI: 10.1007/s10455-026-10028-5
Laurent Manivel
{"title":"(F_4) and desmic quartic surfaces","authors":"Laurent Manivel","doi":"10.1007/s10455-026-10028-5","DOIUrl":"10.1007/s10455-026-10028-5","url":null,"abstract":"<div><p>The desmic pencil of quartic surfaces is part of a beautiful, but mostly forgotten chapter of the classical theory of algebraic surfaces: it is the only non-degenerate pencil of quartic surfaces in <span>({mathbb {P}}^3)</span> containing at least three completely reducible members. We observe in this note that it is closely related to the Weyl group of the root system <span>(F_4)</span>, and can be recovered from a series of symmetric spaces deduced from the exceptional Lie algebras. We discuss the main properties of the pencil from this Lie theoretic point of view.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147335696","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}
引用次数: 0
Heat coefficients of surfaces with curved conical singularities 具有弯曲圆锥奇点曲面的热系数
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2025-12-08 DOI: 10.1007/s10455-025-10024-1
Dorothee Schueth
{"title":"Heat coefficients of surfaces with curved conical singularities","authors":"Dorothee Schueth","doi":"10.1007/s10455-025-10024-1","DOIUrl":"10.1007/s10455-025-10024-1","url":null,"abstract":"<div><p>Let (<i>M</i>, <i>g</i>) be a two-dimensional Riemannian manifold of finite diameter with a conical singularity. Under the assumption that the metric near the cone point <i>C</i> is rotationally invariant, but not necessarily flat, we give an explicit formula for the coefficient <span>(b_{1/2}(C))</span> in the heat trace expansion <span>(operatorname {tr}(operatorname {exp}(-tDelta _g))sim _{tsearrow 0} (4pi t)^{-1}sum _{j=0}^infty a_j(M) t^j+sum _{j=0}^infty b_{j/2}(C)t^{j/2}+sum _{j=0}^infty c_{j/2}(C) t^{j/2} log t)</span>. In the case that the Gaussian curvature <i>K</i> of (<i>M</i>, <i>g</i>) satisfies <span>(|K(p)|rightarrow infty )</span> as <span>(prightarrow C)</span>, we show that <span>(b_{1/2}(C))</span> varies irrationally under constant rescalings of the distance circles near the cone point. This is a sharp contrast to the behavior of <span>(b_0(C))</span> and of those coefficients <span>(b_j(C))</span> which appear in certain known formulas in the case of orbifold cone points or corners of geodesic polygons.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145729883","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}
引用次数: 0
Tetraplectic structures compatible with local quaternionic toric actions 与局部四元数环作用相容的四塑性结构
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2025-11-07 DOI: 10.1007/s10455-025-10023-2
Panagiotis Batakidis, Ioannis Gkeneralis
{"title":"Tetraplectic structures compatible with local quaternionic toric actions","authors":"Panagiotis Batakidis,&nbsp;Ioannis Gkeneralis","doi":"10.1007/s10455-025-10023-2","DOIUrl":"10.1007/s10455-025-10023-2","url":null,"abstract":"<div><p>This paper introduces a quaternionic analogue of toric geometry by developing the theory of local <span>( Q^n := textrm{Sp}(1)^n )</span>-actions on <span>( 4n )</span>-dimensional manifolds, modeled on the regular representation. We identify obstructions that measure the failure of local properties to globalize and define two invariants: a combinatorial invariant called the characteristic pair and a cohomological invariant called the Euler class, which together classify local quaternionic torus actions up to homeomorphism. We also study tetraplectic structures in quaternionic toric geometry by introducing locally generalized Lagrangian-type toric fibrations and show that such fibrations are locally modeled on <span>( mathbb {R}^n times Q^n )</span> using a quaternionic version of the Arnold–Liouville theorem. In the last part, we show that orbit spaces of these actions acquire the structure of quaternionic integral affine manifolds with corners and Lagrangian overlaps, and we classify such spaces by establishing a quaternionic Delzant-type theorem.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145449513","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}
引用次数: 0
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