Annals of Global Analysis and Geometry最新文献

{"title":"Some rigidity results for static three-manifolds with boundary and positive scalar curvature","authors":"Vladimir Medvedev","doi":"10.1007/s10455-026-10056-1","DOIUrl":"10.1007/s10455-026-10056-1","url":null,"abstract":"<div><p>This paper studies three-dimensional compact static manifolds with boundary and positive scalar curvature. We prove that, under a suitable bound on the Ricci curvature, the orientable quotient of the Nariai static manifold with boundary <span>(Nar_{-1,1}(mathbb {S}^2))</span> is the only such manifold with connected boundary, provided that the zero-level set of the potential is connected and does not intersect the boundary. We also establish a rigidity theorem for the upper hemisphere with the standard static potential, in the spirit of Cruz and Nunes.\u0000</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"70 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148750985","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 compact solvmanifolds with left-invariant complex structures","authors":"Takumi Yamada","doi":"10.1007/s10455-026-10053-4","DOIUrl":"10.1007/s10455-026-10053-4","url":null,"abstract":"<div><p>We investigate complex geometric properties of compact complex solvmanifolds endowed with left-invariant complex structures, focusing on the case where these manifolds admit a complex parallelizable solvmanifold as a finite covering. While our previous paper examined differences among complex solvmanifolds admitting a common complex parallelizable solvmanifold as a finite covering, the present paper is devoted to the study of their common geometric properties.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"70 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614034","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":"A Willmore-type inequality for hypersurfaces with asymptotic or integral Ricci curvature bounds","authors":"Jihye Lee","doi":"10.1007/s10455-026-10054-3","DOIUrl":"10.1007/s10455-026-10054-3","url":null,"abstract":"<div><p>We establish Willmore-type inequalities for bounded domains in complete non-compact Riemannian manifolds, under either asymptotic or integral Ricci curvature bounds. Those results recover a recent inequality of Jin-Yin [12, Theorem 1.3].</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"70 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-026-10054-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148465871","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}

{"title":"Crowned Lie groups and nets of real subspaces","authors":"Daniel Beltiţă,&nbsp;Karl-Hermann Neeb","doi":"10.1007/s10455-026-10052-5","DOIUrl":"10.1007/s10455-026-10052-5","url":null,"abstract":"<div><p>We introduce the notion of a complex crown domain for a connected Lie group <i>G</i>, and we use analytic extensions of orbit maps of antiunitary representations to these domains to construct nets of real subspaces on <i>G</i> that are isotone, covariant and satisfy the Reeh–Schlieder and Bisognano–Wichmann conditions from Algebraic Quantum Field Theory. This provides a unifying perspective on various constructions of such nets. The representation theoretic properties of different crowns are discussed in some detail for the non-abelian 2-dimensional Lie group <span>(mathop {textrm{Aff}}nolimits ({mathbb R}))</span>. We also characterize the existence of nets with the above properties by a regularity condition in terms of an Euler element in the Lie algebra <span>({mathfrak g})</span> and show that all antiunitary representations of the split oscillator group have this property.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"70 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148389038","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":"Semi-Riemannian (text {spin}^c) manifolds carrying generalized Killing spinors and the classification of Riemannian (text {spin}^c) manifolds admitting a type I imaginary generalized Killing spinor","authors":"Samuel Lockman","doi":"10.1007/s10455-026-10051-6","DOIUrl":"10.1007/s10455-026-10051-6","url":null,"abstract":"<div><p>We classify Riemannian <span>(text {spin}^c)</span> manifolds carrying a type I imaginary generalized Killing spinor, by explicitly constructing a parallel spinor on each leaf of the canonical foliation given by the Dirac current. We also provide a class of Riemannian <span>(text {spin}^c)</span> manifolds carrying a type II imaginary generalized Killing spinor, by considering spacelike hypersurfaces of Lorentzian <span>(text {spin}^c)</span> manifolds. We carry out much of the work in the setting of semi-Riemannian <span>(text {spin}^c)</span>-manifolds carrying generalized Killing spinors, allowing us to draw conclusions in this setting as well. In this context, the Dirac current is not always a closed vector field. We circumvent this in even dimensions, by considering a modified Dirac current, which is closed in the cases when the original Dirac current is not. On the path to these results, we also study semi-Riemannian manifolds carrying closed and conformal vector fields.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"70 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-026-10051-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148323073","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}

{"title":"An Aubin-Yau theorem for transversally Kähler foliations","authors":"Vlad Marchidanu","doi":"10.1007/s10455-026-10049-0","DOIUrl":"10.1007/s10455-026-10049-0","url":null,"abstract":"<div><p>Transversally Kähler foliations are a generalisation of Kähler manifolds, appearing naturally in the complex non-Kähler setting. We give a self-contained proof of how the classical methods used in the proof of the Aubin-Yau theorem adapt to the transversally Kähler case under the homological orientability condition. We apply this result to obtain a new, simpler proof of the already known Vaisman Aubin-Yau theorem.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"70 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-026-10049-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148281362","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}

{"title":"On the Geometry of Cotton Gravity","authors":"Giulio Colombo,&nbsp;Filippo Mastropietro,&nbsp;Marco Rigoli","doi":"10.1007/s10455-026-10048-1","DOIUrl":"10.1007/s10455-026-10048-1","url":null,"abstract":"<div><p>We analyze the geometry of the field equations of Cotton gravity (for a quite general energy-momentum tensor) on a static space-time. In particular, we describe the local structure of the spatial Riemannian factor. This structure, that we call <i>Cotton-</i><span>(varphi )</span><i>-perfect fluid</i> (C-<span>(varphi )</span>-PF, for shorts) is a generalization to the regime of Cotton Gravity of the recently introduced notion of <span>(varphi )</span>-static perfect fluid space-time (<span>(varphi )</span>-SPFST). After discussing the variational origin of this system, we provide sufficient conditions for a C-<span>(varphi )</span>-PF to reduce to a <span>(varphi )</span>-SPFST. We also study the geometry of the level sets of the lapse function <i>f</i> and we provide a rigidity result for C-<span>(varphi )</span>-PFs under some curvature conditions. The role that Codazzi tensors hold in this theory is highlighted.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"70 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148193856","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":"Real hypersurfaces with cyclic parallel normal Jacobi operator in non-flat quaternionic space forms","authors":"Jin Hong Kim,&nbsp;Hyunjin Lee,&nbsp;Young Jin Suh","doi":"10.1007/s10455-026-10042-7","DOIUrl":"10.1007/s10455-026-10042-7","url":null,"abstract":"<div><p>In this paper, we investigate the properties of the normal Jacobi operator of a real hypersurface in non-flat quaternionic space forms, focused on cyclic parallelism and Codazzi type properties. We classify real hypersurfaces that satisfy these properties. As a solution of the classification problem for such real hypersurfaces, we present the following results: Firstly, we prove that a real hypersurface satisfying a certain condition for the normal Jacobi operator is curvature-adapted. Based on this fact, we further show that in the quaternionic hyperbolic space, the shape operator <i>A</i> of <i>M</i> commutes with the three structure tensors <span>(phi _{nu })</span>, <span>(nu =1,2,3)</span>, of <i>M</i> on the maximal quaternionic subbundle <span>(mathfrak D)</span>.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"70 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148193857","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":"Remarks on quasi-Sasakian structures","authors":"Emmanuel Gnandi,&nbsp;Fortuné Massamba","doi":"10.1007/s10455-026-10047-2","DOIUrl":"10.1007/s10455-026-10047-2","url":null,"abstract":"<div><p>In this work, we revisit quasi-Sasakian structures in dimension three and examine how these structures interact with the foliation generated by the Reeb vector field and its basic cohomology. Through a deformation-based approach, we show that a closed, orientable 3-manifold admits a quasi-Sasakian structure precisely when it is either Sasakian or arises as a Kähler mapping torus. In particular, every quasi-Sasakian structure in this setting can be deformed into a Sasakian or a co-Kähler one. This result leads to a complete classification of quasi-Sasakian manifolds in dimension three and highlights the geometric and topological features that distinguish the two cases.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172161","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":"Existence of conical higher cscK metrics on a minimal ruled surface","authors":"Rajas Sandeep Sompurkar","doi":"10.1007/s10455-026-10046-3","DOIUrl":"10.1007/s10455-026-10046-3","url":null,"abstract":"<div><p>A ‘higher extremal Kähler metric’ is defined (motivated by analogy with the definition of an extremal Kähler metric) as a Kähler metric whose top Chern form equals a globally defined smooth function multiplied by its volume form such that the gradient of the smooth function is a holomorphic vector field. A special case of this kind of metric is a ‘higher constant scalar curvature Kähler (higher cscK) metric’ which is defined (again by analogy with the definition of a constant scalar curvature Kähler (cscK) metric) as one whose top Chern form is a constant multiple of its volume form or equivalently whose top Chern form is harmonic. In our previous paper on higher extremal Kähler metrics we had looked at a certain class of minimal ruled surfaces called as ‘pseudo-Hirzebruch surfaces’ all of which contain two special divisors (viz. the zero and infinity divisors) and serve as the primary example manifolds in the momentum construction method (the Calabi ansatz procedure) which is used for producing explicit examples of the above-mentioned kinds of canonical Kähler metrics. We had proven that every Kähler class on such a surface admits a momentum-constructed higher extremal Kähler metric which is not higher cscK and we had further proven by using the ‘top Bando-Futaki invariant’ that higher cscK metrics do not exist in any Kähler class on the surface. In this paper we will see that if we allow our metrics to develop ‘conical singularities’ along at least one of the two special divisors of the surface then we do get ‘conical higher cscK metrics’ in each Kähler class of the surface by the momentum construction method. We will show that our constructed metrics satisfy the “polyhomogeneous condition” for conical Kähler metrics and we will interpret the conical higher cscK equation “globally on the surface” in terms of the currents of integration along the zero and infinity divisors. We will introduce the ‘top <span>(log )</span> Bando-Futaki invariant’ and then try to prove some standard expected results about it, with the final aim being to employ it to arrive at a certain linear relationship, that we conjecture must exist, between the cone angles of the conical singularities along the zero and infinity divisors.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148173438","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}