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Annals of Global Analysis and Geometry最新文献

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On the curvature and topology of compact stationary spacetimes 紧定时空的曲率与拓扑
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2026-05-03 DOI: 10.1007/s10455-026-10029-4
Amir Babak Aazami
{"title":"On the curvature and topology of compact stationary spacetimes","authors":"Amir Babak Aazami","doi":"10.1007/s10455-026-10029-4","DOIUrl":"10.1007/s10455-026-10029-4","url":null,"abstract":"<div><p>Using the result of Petersen &amp; Wink ’21, we find obstructions to the curvature and topology of compact Lorentzian manifolds admitting a unit-length timelike Killing vector field.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147807605","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
Computer-assisted construction of SU(2)-invariant negative Einstein metrics SU(2)不变负爱因斯坦度量的计算机辅助构造
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2026-04-29 DOI: 10.1007/s10455-026-10037-4
Qiu Shi Wang
{"title":"Computer-assisted construction of SU(2)-invariant negative Einstein metrics","authors":"Qiu Shi Wang","doi":"10.1007/s10455-026-10037-4","DOIUrl":"10.1007/s10455-026-10037-4","url":null,"abstract":"<div><p>We construct a 2-parameter family of new triaxial <i>SU</i>(2)-invariant complete negative Einstein metrics on the complex line bundle <span>(mathcal {O}(-4))</span> over <span>(mathbb {C}P^1)</span>. The metrics are conformally compact and neither Kähler nor self-dual. The proof involves using rigorous numerics to produce an approximate Einstein metric to high precision in a bounded region containing the singular orbit or “bolt”, which is then perturbed to a genuine Einstein metric using fixed-point methods. At the boundary of this region, the latter metric is sufficiently close to hyperbolic space for us to show that it indeed extends to a complete, asymptotically hyperbolic Einstein metric.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-026-10037-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147797022","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
Parallel differential forms of codegree two, and three-forms in dimension six 二次余数的平行微分形式，以及六维的三维形式
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2026-04-17 DOI: 10.1007/s10455-026-10040-9
Andrzej Derdzinski, Paolo Piccione, Ivo Terek
{"title":"Parallel differential forms of codegree two, and three-forms in dimension six","authors":"Andrzej Derdzinski,&nbsp;Paolo Piccione,&nbsp;Ivo Terek","doi":"10.1007/s10455-026-10040-9","DOIUrl":"10.1007/s10455-026-10040-9","url":null,"abstract":"<div><p>For a differential form on a manifold, having constant components in suitable local coordinates trivially implies being parallel relative to a torsion-free connection, and the converse implication is known to be true for <i>p</i>-forms in dimension <i>n</i> when <span>(p=0,1,2,n-1,n)</span>. We prove the converse for <span>((n-2))</span>-forms, and for 3-forms when <span>(n=6)</span>, while pointing out that it fails to hold for Cartan 3-forms on all simple Lie groups of dimensions <span>(nge 8)</span> as well as for <span>((n,p)=(7,3))</span> and <span>((n,p)=(8,4))</span>, where the 3-forms and 4-forms arise in compact simply connected Riemannian manifolds with exceptional holonomy groups. We also provide geometric characterizations of 3-forms in dimension six and <span>((n-2))</span>-forms in dimension <i>n</i> having the constant-components property mentioned above, and describe examples illustrating the fact that various parts of these geometric characterizations are logically independent.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-026-10040-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147737756","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
Complex structures of the Gibbons-Hawking ansatz with infinite topological type 具有无限拓扑型的Gibbons-Hawking ansatz复杂结构
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2026-04-15 DOI: 10.1007/s10455-026-10039-2
Wenxin He, Bin Xu
{"title":"Complex structures of the Gibbons-Hawking ansatz with infinite topological type","authors":"Wenxin He,&nbsp;Bin Xu","doi":"10.1007/s10455-026-10039-2","DOIUrl":"10.1007/s10455-026-10039-2","url":null,"abstract":"<div><p>In this paper, we study the complex structures of complete hyperkähler four-manifolds of infinite topological type arising from the Gibbons-Hawking ansatz. We show that for almost all complex structures in the hyperkähler family, the manifold is biholomorphic to a hypersurface in <span>(mathbb {C}^3)</span> defined by an explicit entire function. For the remaining complex structures, we further prove that the manifold is biholomorphic to the minimal resolution of a singular surface in <span>(mathbb {C}^3)</span> under certain conditions. Thus, we partially extend LeBrun’s celebrated work [LeBrun, C.: Complete Ricci-flat Kähler metrics on <span>(mathbb {C} ^n)</span> need not be flat. In Proc. Symp. Pure Math <b>52</b>, 297–304 (1991)] to the context of countably many punctures.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147737786","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
Invariants of stably trivial vector bundles with connection 具有连接的稳定平凡向量束的不变量
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2026-04-08 DOI: 10.1007/s10455-026-10041-8
Sergiu Moroianu
{"title":"Invariants of stably trivial vector bundles with connection","authors":"Sergiu Moroianu","doi":"10.1007/s10455-026-10041-8","DOIUrl":"10.1007/s10455-026-10041-8","url":null,"abstract":"<div><p>We define a Chern–Simons invariant of connections on stably trivial vector bundles over smooth manifolds, taking values in 3-forms modulo closed forms with integral cohomology class. We show an additivity property of this invariant for connections defined on a direct sum of bundles, under a certain block-diagonality condition on the curvature. As a corollary, we deduce an obstruction for conformally immersing a <i>n</i>-dimensional Riemannian manifold in a translation manifold of dimension <span>(n+1)</span>.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147642361","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 splittings of deformations of pairs of complex structures and holomorphic vector bundles 复结构对与全纯向量束变形的分裂
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2026-04-03 DOI: 10.1007/s10455-026-10036-5
Hisashi Kasuya, Valto Purho
{"title":"On splittings of deformations of pairs of complex structures and holomorphic vector bundles","authors":"Hisashi Kasuya,&nbsp;Valto Purho","doi":"10.1007/s10455-026-10036-5","DOIUrl":"10.1007/s10455-026-10036-5","url":null,"abstract":"<div><p>We can show that the Kuranishi space of a pair (<i>M</i>, <i>E</i>) of a compact Kähler manifold <i>M</i> and its flat Hermitian vector bundle <i>E</i> is isomorphic to the direct product of the Kuranishi space of <i>M</i> and the Kuranishi space of <i>E</i>. We study non-Kähler case. We show that the Kuranishi space of a pair (<i>M</i>, <i>E</i>) of a complex parallelizable nilmanifold <i>M</i> and its trivial holomorphic vector bundle <i>E</i> is isomorphic to the direct product of the Kuranishi space of <i>M</i> and the Kuranishi space of <i>E</i>. We give examples of pairs (<i>M</i>, <i>E</i>) of nilmanifolds <i>M</i> with left-invariant abelian complex structures and their trivial holomorphic line bundles <i>E</i> such that the Kuranishi spaces of pairs (<i>M</i>, <i>E</i>) are not isomorphic to direct products of the Kuranishi spaces of <i>M</i> and the Kuranishi spaces of <i>E</i>.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147588386","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 parallel transport map over reductive homogeneous space 约化齐次空间上的平行运输映射
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2026-03-30 DOI: 10.1007/s10455-026-10038-3
Masahiro Morimoto
{"title":"The parallel transport map over reductive homogeneous space","authors":"Masahiro Morimoto","doi":"10.1007/s10455-026-10038-3","DOIUrl":"10.1007/s10455-026-10038-3","url":null,"abstract":"<div><p>We show that the parallel transport map over a reductive homogeneous space with natural torsion-free connection becomes an affine submersion with horizontal distribution. This generalizes one of the main results in the author’s previous paper in the case of affine symmetric spaces. We also prove the compactness of the shape operators of the submanifold lifted by the parallel transport map. This improves a previous result by the author and generalizes some results of Terng-Thorbergsson and of Koike. Furthermore we propose two definitions for the regularized mean curvatures of affine Fredholm submanifolds in Hilbertable spaces and discuss their relations to the parallel transport map. In particular, each fiber of the parallel transport map over a reductive homogeneous space is shown to be minimal in both senses.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-026-10038-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147607404","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
Quantization of the Kähler-Ricci flow and optimal destabilizer for a Fano manifold 法诺流形Kähler-Ricci流的量化和最优不稳定器
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2026-03-19 DOI: 10.1007/s10455-025-10025-0
Tomoyuki Hisamoto
{"title":"Quantization of the Kähler-Ricci flow and optimal destabilizer for a Fano manifold","authors":"Tomoyuki Hisamoto","doi":"10.1007/s10455-025-10025-0","DOIUrl":"10.1007/s10455-025-10025-0","url":null,"abstract":"<div><p>For a Fano manifold, We consider the geometric quantization of the Kähler-Ricci flow and the associated entropy functional. Convergence to the original flow and entropy is established. Based on these results we formulate the finite-dimensional approximation of the optimal degeneration for the anti-canonical polarization.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560241","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 local moduli of Sasaki-Einstein rational homology 7-spheres and invertible polynomials Sasaki-Einstein有理同调7球与可逆多项式的局部模
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2026-03-17 DOI: 10.1007/s10455-026-10035-6
Jaime Cuadros Valle, Joe Lope Vicente
{"title":"The local moduli of Sasaki-Einstein rational homology 7-spheres and invertible polynomials","authors":"Jaime Cuadros Valle,&nbsp;Joe Lope Vicente","doi":"10.1007/s10455-026-10035-6","DOIUrl":"10.1007/s10455-026-10035-6","url":null,"abstract":"<div><p>We study the local moduli space of Sasaki-Einstein metrics on links of invertible polynomials defining rational homology 7-spheres. All these polynomials are either of cycle type or are given as Thom Sebastiani sums of a cycle block and another atomic block. We found that for polynomials of cycle type, the local moduli spaces of Sasaki-Einstein metrics are zero dimensional. For the Thom-Sebastiani sums of an atomic block and a cycle polynomial, the dimensions of the local moduli spaces of Sasaki-Einstein metrics are positive in general. Since all the links under study in this article remain Sasaki-Einstein rational homology 7-spheres under the Berglund-Hübsch rule from classical mirror symmetry (Berglund and Hübsch, Nucl Phys B 393:377–391 (1993), Cuadros et al., Commun Math Phys 405:199 (2024)), we are able to find solutions for the problem associated to the moduli for the Berglund-Hübsch transpose duals of this type of links. For the purpose of doing this, we give specific description of the moduli spaces of complex structures on the weighted quasismooth hypersurfaces cut out by the corresponding invertible polynomials and, in particular, from this description, we can produce families of quasismooth weighted hypersurfaces that degenerate to non-quasismooth with at worst klt singularities.</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":"147560085","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
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
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