Journal of Geometry and Physics最新文献

{"title":"Anti-invariant Riemannian maps from Sasakian manifolds and Clairaut condition","authors":"Reetu Maini ,&nbsp;Garima Gupta ,&nbsp;Rashmi Sachdeva ,&nbsp;Rakesh Kumar ,&nbsp;Rachna Rani ,&nbsp;Satvinder Singh Bhatia","doi":"10.1016/j.geomphys.2025.105581","DOIUrl":"10.1016/j.geomphys.2025.105581","url":null,"abstract":"<div><div>We study anti-invariant Riemannian maps from Sasakian manifolds to Riemannian manifolds, focusing on the case where the structure vector field is horizontal. We investigate Clairaut anti-invariant Riemannian maps from Sasakian manifolds to Riemannian manifolds and derive a condition under which an anti-invariant Riemannian map becomes a Clairaut Riemannian map. We also present non-trivial examples of anti-invariant and Clairaut anti-invariant Riemannian maps from Sasakian manifolds to Riemannian manifolds, ensuring the structure vector field remains horizontal.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105581"},"PeriodicalIF":1.6,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144569976","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":"Rota-Baxter operators on cocommutative Hopf algebras and Hopf braces","authors":"Huihui Zheng ,&nbsp;Liangyun Zhang ,&nbsp;Tianshui Ma ,&nbsp;Li Guo","doi":"10.1016/j.geomphys.2025.105580","DOIUrl":"10.1016/j.geomphys.2025.105580","url":null,"abstract":"<div><div>This paper studies the relationship of Rota-Baxter operators on cocommutative Hopf algebras with Hopf braces and the Yang-Baxter equation, with emphasis on the embedding of cocommutative Hopf braces into Rota-Baxter Hopf algebras. Through Hopf braces, we establish a connection between relative Rota-Baxter operators on cocommutative Hopf algebras and bijective 1-cocycles. Finally, we introduce the notion of symmetric Hopf braces, and establish the relationship between symmetric Hopf braces and Rota-Baxter Hopf algebras.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105580"},"PeriodicalIF":1.6,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144588693","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":"Generating functions for irreversible Hamiltonian systems","authors":"Dan Goreac ,&nbsp;Jonas Kirchhoff ,&nbsp;Bernhard Maschke","doi":"10.1016/j.geomphys.2025.105578","DOIUrl":"10.1016/j.geomphys.2025.105578","url":null,"abstract":"<div><div>The definition of conservative-irreversible functions is extended to smooth manifolds. Local representation of these functions is studied and reveals that they can not necessarily be given as the weighted product of almost Poisson brackets, but as the sum of such. The biquadratic functions induced by conservative-irreversible functions are studied and demonstrate a possibility for an algebraic framework on arbitrary and in particular complex algebras.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105578"},"PeriodicalIF":1.6,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144588695","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-weight modules over the generalized mirror Heisenberg-Virasoro algebra of rank two","authors":"Xinwei Gu ,&nbsp;Jiancai Sun","doi":"10.1016/j.geomphys.2025.105577","DOIUrl":"10.1016/j.geomphys.2025.105577","url":null,"abstract":"<div><div>In this paper, we investigate non-weight modules over the generalized mirror Heisenberg-Virasoro algebra of rank two, denoted <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span>, where <span><math><mi>p</mi><mo>,</mo><mi>q</mi><mo>∈</mo><mi>C</mi></math></span>. We construct a family of irreducible modules over this algebra, classify their isomorphism classes, and rigorously demonstrate that these modules exhaustively characterize all <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span>-modules that are <span><math><mi>U</mi><mo>(</mo><mi>h</mi><mo>)</mo></math></span>-free modules of rank 1, with <span><math><mi>h</mi></math></span> being the Cartan subalgebra.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105577"},"PeriodicalIF":1.6,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144569975","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":"The symmetry regularization of 1D generalized Kepler problems","authors":"Junwei Ma,&nbsp;Guowu Meng,&nbsp;Jiazhuo Xiao","doi":"10.1016/j.geomphys.2025.105576","DOIUrl":"10.1016/j.geomphys.2025.105576","url":null,"abstract":"<div><div>The 1D generalized Kepler problem with magnetic charge <span><math><mi>μ</mi><mo>≥</mo><mn>0</mn></math></span> is the Hamiltonian system for which the phase space is the total cotangent space of the half line <span><math><msub><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>:</mo><mo>=</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo></math></span> and the Hamiltonian is <span><math><mi>H</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><msup><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mfrac><mrow><msup><mrow><mi>μ</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>2</mn><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>q</mi></mrow></mfrac></math></span> where <span><math><mi>q</mi><mo>∈</mo><msub><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span> is the position and <span><math><mi>p</mi><mo>∈</mo><mi>R</mi></math></span> is the momentum. Let <span><math><msub><mrow><mi>Σ</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span> be the positive portion of the phase space (i.e., <span><math><mo>{</mo><mi>H</mi><mo>&gt;</mo><mn>0</mn><mo>}</mo></math></span>) and <span><math><msub><mrow><mi>Σ</mi></mrow><mrow><mo>−</mo></mrow></msub></math></span> be the negative portion of the phase space. Denote by <span><math><msub><mrow><mi>O</mi></mrow><mrow><mi>a</mi></mrow></msub></math></span> the co-adjoint orbit of <span><math><msub><mrow><mi>sl</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo><mo>≡</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msup></math></span> defined by conditions <span><math><msubsup><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>−</mo><msubsup><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>−</mo><msubsup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&gt;</mo><mn>0</mn></math></span>. It is demonstrated that there is a symplectic embedding <span><math><msub><mrow><mi>ι</mi></mrow><mrow><mo>−</mo></mrow></msub></math></span>: <span><math><msub><mrow><mi>Σ</mi></mrow><mrow><mo>−</mo></mrow></msub><mo>→</mo><msub><mrow><mi>O</mi></mrow><mrow><mi>μ</mi></mrow></msub></math></span> such that the image of <span><math><msub><mrow><mi>ι</mi></mrow><mrow><mo>−</mo></mrow></msub></math></span> is dense and open, and any Kepler motion (i.e. Hamiltonian motion under <em>H</em>) inside <span><math><msub><mrow><mi>Σ</mi></mrow><mrow><mo>−</mo></mrow></msub></math></span>, after being embedded via <span><math><msub><mrow><mi>ι</mi></mrow><mrow><mo>−</mo></mrow></msub></math></span>, extends to a complete Hamiltonian motion inside <span><math><msub><mrow><mi>O</mi></","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105576"},"PeriodicalIF":1.6,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144523058","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 naturally reductive Einstein metrics on SU(N) via generalized flag manifolds","authors":"Andreas Arvanitoyeorgos ,&nbsp;Yusuke Sakane ,&nbsp;Marina Statha","doi":"10.1016/j.geomphys.2025.105575","DOIUrl":"10.1016/j.geomphys.2025.105575","url":null,"abstract":"<div><div>We obtain new invariant Einstein metrics on the compact Lie group <span><math><mi>SU</mi><mo>(</mo><mi>N</mi><mo>)</mo></math></span> which are not naturally reductive. This is achieved by using the generalized flag manifold <span><math><mi>G</mi><mo>/</mo><mi>K</mi><mo>=</mo><mi>SU</mi><mo>(</mo><msub><mrow><mi>k</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><mo>⋯</mo><mo>+</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>)</mo><mo>/</mo><mi>S</mi><mo>(</mo><mi>U</mi><mo>(</mo><msub><mrow><mi>k</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo><mo>×</mo><mo>⋯</mo><mo>×</mo><mi>U</mi><mo>(</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>)</mo><mo>)</mo></math></span> and by taking an appropriate choice of orthogonal basis of the center of the Lie subalgebra <span><math><mi>k</mi></math></span> for <em>K</em>, which poses certain symmetry conditions to the <span><math><mi>Ad</mi><mo>(</mo><mi>K</mi><mo>)</mo></math></span>-invariant metrics of <span><math><mi>SU</mi><mo>(</mo><mi>N</mi><mo>)</mo></math></span>. We also study the isometry problem for the Einstein metrics found.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105575"},"PeriodicalIF":1.6,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144523059","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-split superstrings of dimension (1|2)","authors":"Dimitry Leites ,&nbsp;Alexander S. Tikhomirov","doi":"10.1016/j.geomphys.2025.105579","DOIUrl":"10.1016/j.geomphys.2025.105579","url":null,"abstract":"<div><div>Any supermanifold diffeomorphic to one whose structure sheaf is the sheaf of sections of the exterior algebra of a vector bundle <strong>E</strong> over the underlying manifold <em>M</em> is called split. Gawȩdzki (1977) and Batchelor (1979) were the first to prove that any smooth supermanifold is split. In 1981, P. Green, and Palamodov, found examples of non-split analytic supermanifolds and described obstructions to splitness that were further studied by Manin (resp., Onishchik with his students) following Palamodov's (resp., Green's) approach. Following Palamodov, Donagi and Witten demonstrated that some of the moduli supervarieties of superstring theories are non-split. Except for <span><span>arXiv:2210.17096</span><svg><path></path></svg></span>, the odd parameters of supervarieties of obstructions to splitness were never considered. Here, using Palamodov's approach, we classify and describe the even (degree-2) and the odd (degree-1) obstructions to splitness of <span><math><mo>(</mo><mn>1</mn><mo>|</mo><mn>2</mn><mo>)</mo></math></span>-dimensional superstrings. In particular, we correct calculations of degree-2 obstructions due to Bunegina and Onishchik and confirm Manin's answer, but correct his description of the group <span><math><mtext>Aut</mtext><mo>(</mo><mtext>E</mtext><mo>)</mo></math></span>.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105579"},"PeriodicalIF":1.6,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144549358","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":"Classification results for totally real surfaces of nearly Kähler CP3","authors":"Michaël Liefsoens ,&nbsp;Hui Ma ,&nbsp;Luc Vrancken","doi":"10.1016/j.geomphys.2025.105574","DOIUrl":"10.1016/j.geomphys.2025.105574","url":null,"abstract":"<div><div>Totally real surfaces in the nearly Kähler <span><math><mi>C</mi><msup><mrow><mi>P</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> are investigated and are completely classified under various additional assumptions, resulting in multiple new examples. Among others, the classification includes totally real surfaces that are extrinsically homogeneous; or minimal; or totally umbilical; or Codazzi-like (including parallel and non-parallel examples).</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105574"},"PeriodicalIF":1.6,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144549356","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":"Symmetric separation of variables, shifted spectral curves and classical r-matrices","authors":"T. Skrypnyk","doi":"10.1016/j.geomphys.2025.105573","DOIUrl":"10.1016/j.geomphys.2025.105573","url":null,"abstract":"<div><div>We develop a method of separating functions in the theory of variable separation for the Lax-integrable hamiltonian systems. For the case of <span><math><mi>g</mi><mi>l</mi><mo>(</mo><mn>2</mn><mo>)</mo></math></span>-valued Lax matrices we propose a modified approach to construction of separating functions leading to shifted spectral curves of the initial Lax matrices. In particular, we construct one-parametric families of separated variables for the classical hamiltonian systems governed by three classes of non-skew-symmetric, non-dynamical <span><math><mi>g</mi><mi>l</mi><mo>(</mo><mn>2</mn><mo>)</mo><mo>⊗</mo><mi>g</mi><mi>l</mi><mo>(</mo><mn>2</mn><mo>)</mo></math></span>-valued classical <em>r</em>-matrices of the rational and trigonometric type. We show that for almost all <em>r</em>-matrices in the considered families the corresponding curves of separation are shifted spectral curves of the initial Lax matrices. The proposed scheme is illustrated by the examples of separation of variables for the integrable cases of the Kirckhoff problem based on the Lie algebra <span><math><mi>g</mi><mi>l</mi><mo>(</mo><mn>2</mn><mo>)</mo></math></span> and on the considered families of the classical <em>r</em>-matrices.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105573"},"PeriodicalIF":1.6,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144513904","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":"Addendum to “Six dimensional homogeneous spaces with holomorphically trivial canonical bundle” [J. Geom. Phys. 194 (2023) 105014]","authors":"Antonio Otal ,&nbsp;Luis Ugarte","doi":"10.1016/j.geomphys.2025.105570","DOIUrl":"10.1016/j.geomphys.2025.105570","url":null,"abstract":"<div><div>In this note we focus on the complex Hermitian geometry of a solvable Lie algebra that was missing in our recent paper “Six dimensional homogeneous spaces with holomorphically trivial canonical bundle”. We prove that it supports a unique complex structure with non-zero closed (3,0)-form, and we describe its space of balanced Hermitian metrics. The non-existence of instantons associated to any invariant balanced Hermitian metric on solvmanifolds constructed from that Lie algebra is also proved.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105570"},"PeriodicalIF":1.6,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144322409","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}