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Modular geodesics and wedge domains in non-compactly causal symmetric spaces 非紧密因果对称空间中的模块大地线和楔域
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-12-31 DOI: 10.1007/s10455-023-09937-6
Vincenzo Morinelli, Karl-Hermann Neeb, Gestur Ólafsson
{"title":"Modular geodesics and wedge domains in non-compactly causal symmetric spaces","authors":"Vincenzo Morinelli,&nbsp;Karl-Hermann Neeb,&nbsp;Gestur Ólafsson","doi":"10.1007/s10455-023-09937-6","DOIUrl":"10.1007/s10455-023-09937-6","url":null,"abstract":"<div><p>We continue our investigation of the interplay between causal structures on symmetric spaces and geometric aspects of Algebraic Quantum Field Theory. We adopt the perspective that the geometric implementation of the modular group is given by the flow generated by an Euler element of the Lie algebra (an element defining a 3-grading). Since any Euler element of a semisimple Lie algebra specifies a canonical non-compactly causal symmetric space <span>(M = G/H)</span>, we turn in this paper to the geometry of this flow. Our main results concern the positivity region <i>W</i> of the flow (the corresponding wedge region): If <i>G</i> has trivial center, then <i>W</i> is connected, it coincides with the so-called observer domain, specified by a trajectory of the modular flow which at the same time is a causal geodesic. It can also be characterized in terms of a geometric KMS condition, and it has a natural structure of an equivariant fiber bundle over a Riemannian symmetric space that exhibits it as a real form of the crown domain of <i>G</i>/<i>K</i>. Among the tools that we need for these results are two observations of independent interest: a polar decomposition of the positivity domain and a convexity theorem for <i>G</i>-translates of open <i>H</i>-orbits in the minimal flag manifold specified by the 3-grading.\u0000</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09937-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139061323","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
Immersions of Sasaki–Ricci solitons into homogeneous Sasakian manifolds 佐佐木-里奇孤子在均质佐佐木流形中的沉浸
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-12-14 DOI: 10.1007/s10455-023-09939-4
R. Mossa, G. Placini
{"title":"Immersions of Sasaki–Ricci solitons into homogeneous Sasakian manifolds","authors":"R. Mossa,&nbsp;G. Placini","doi":"10.1007/s10455-023-09939-4","DOIUrl":"10.1007/s10455-023-09939-4","url":null,"abstract":"<div><p>We discuss local Sasakian immersion of Sasaki–Ricci solitons (SRS) into fiber products of homogeneous Sasakian manifolds. In particular, we prove that SRS locally induced by a large class of fiber products of homogeneous Sasakian manifolds are, in fact, <span>(eta )</span>-Einstein. The results are stronger for immersions into Sasakian space forms. Moreover, we show an example of a Kähler–Ricci soliton on <span>(mathbb C^n)</span> which admits no local holomorphic isometry into products of homogeneous bounded domains with flat Kähler manifolds and generalized flag manifolds.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138631126","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
Optimal transport approach to Michael–Simon–Sobolev inequalities in manifolds with intermediate Ricci curvature lower bounds 具有中间里奇曲率下限的流形中迈克尔-西蒙-索博廖夫不等式的最优传输方法
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-12-13 DOI: 10.1007/s10455-023-09934-9
Kai-Hsiang Wang
{"title":"Optimal transport approach to Michael–Simon–Sobolev inequalities in manifolds with intermediate Ricci curvature lower bounds","authors":"Kai-Hsiang Wang","doi":"10.1007/s10455-023-09934-9","DOIUrl":"10.1007/s10455-023-09934-9","url":null,"abstract":"<div><p>We generalize McCann’s theorem of optimal transport to a submanifold setting and use it to prove Michael–Simon–Sobolev inequalities for submanifolds in manifolds with lower bounds on intermediate Ricci curvatures. The results include a variant of the sharp Michael–Simon–Sobolev inequality in Brendle’s (arXiv:2009.13717) when the intermediate Ricci curvatures are nonnegative.\u0000</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138578073","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
From complex contact structures to real almost contact 3-structures 从复杂的接触结构到真实的几乎接触的 3 结构
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-12-12 DOI: 10.1007/s10455-023-09935-8
Eder M. Correa
{"title":"From complex contact structures to real almost contact 3-structures","authors":"Eder M. Correa","doi":"10.1007/s10455-023-09935-8","DOIUrl":"10.1007/s10455-023-09935-8","url":null,"abstract":"<div><p>We prove that every complex contact structure gives rise to a distinguished type of almost contact metric 3-structure. As an application, we provide several new examples of manifolds which admit taut contact circles, taut and round almost cosymplectic 2-spheres, and almost hypercontact (metric) structures. These examples generalize the well-known examples of contact circles defined by the Liouville-Cartan forms on the unit cotangent bundle of Riemann surfaces. Further, we provide sufficient conditions for a compact complex contact manifold to be the twistor space of a positive quaternionic Kähler manifold.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138578040","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
Families of degenerating Poincaré–Einstein metrics on (mathbb {R}^4) 简并的庞加莱姆-爱因斯坦度量的族 $$mathbb {R}^4$$
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-12-06 DOI: 10.1007/s10455-023-09923-y
Carlos A. Alvarado, Tristan Ozuch, Daniel A. Santiago
{"title":"Families of degenerating Poincaré–Einstein metrics on (mathbb {R}^4)","authors":"Carlos A. Alvarado,&nbsp;Tristan Ozuch,&nbsp;Daniel A. Santiago","doi":"10.1007/s10455-023-09923-y","DOIUrl":"10.1007/s10455-023-09923-y","url":null,"abstract":"<div><p>We provide the first example of continuous families of Poincaré–Einstein metrics developing cusps on the trivial topology <span>(mathbb {R}^4)</span>. We also exhibit families of metrics with unexpected degenerations in their conformal infinity only. These are obtained from the Riemannian version of an ansatz of Debever and Plebański–Demiański. We additionally indicate how to construct similar examples on more complicated topologies.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09923-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138507067","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
Commutativity of quantization with conic reduction for torus actions on compact CR manifolds 紧CR流形上环面作用的二次约化量化交换性
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-11-29 DOI: 10.1007/s10455-023-09931-y
Andrea Galasso
{"title":"Commutativity of quantization with conic reduction for torus actions on compact CR manifolds","authors":"Andrea Galasso","doi":"10.1007/s10455-023-09931-y","DOIUrl":"10.1007/s10455-023-09931-y","url":null,"abstract":"<div><p>We define conic reductions <span>(X^{textrm{red}}_{nu })</span> for torus actions on the boundary <i>X</i> of a strictly pseudo-convex domain and for a given weight <span>(nu )</span> labeling a unitary irreducible representation. There is a natural residual circle action on <span>(X^{textrm{red}}_{nu })</span>. We have two natural decompositions of the corresponding Hardy spaces <i>H</i>(<i>X</i>) and <span>(H(X^{textrm{red}}_{nu }))</span>. The first one is given by the ladder of isotypes <span>(H(X)_{knu })</span>, <span>(kin {mathbb {Z}})</span>; the second one is given by the <i>k</i>-th Fourier components <span>(H(X^{textrm{red}}_{nu })_k)</span> induced by the residual circle action. The aim of this paper is to prove that they are isomorphic for <i>k</i> sufficiently large. The result is given for spaces of (0, <i>q</i>)-forms with <span>(L^2)</span>-coefficient when <i>X</i> is a CR manifold with non-degenerate Levi form.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09931-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138454594","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
Sasaki–Einstein 7-manifolds and Orlik’s conjecture Sasaki-Einstein 7-流形和Orlik猜想
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-11-16 DOI: 10.1007/s10455-023-09930-z
Jaime Cuadros Valle, Joe Lope Vicente
{"title":"Sasaki–Einstein 7-manifolds and Orlik’s conjecture","authors":"Jaime Cuadros Valle,&nbsp;Joe Lope Vicente","doi":"10.1007/s10455-023-09930-z","DOIUrl":"10.1007/s10455-023-09930-z","url":null,"abstract":"<div><p>We study the homology groups of certain 2-connected 7-manifolds admitting quasi-regular Sasaki–Einstein metrics, among them, we found 52 new examples of Sasaki–Einstein rational homology 7-spheres, extending the list given by Boyer et al. (Ann Inst Fourier 52(5):1569–1584, 2002). As a consequence, we exhibit new families of positive Sasakian homotopy 9-spheres given as cyclic branched covers, determine their diffeomorphism types and find out which elements do not admit extremal Sasaki metrics. We also improve previous results given by Boyer (Note Mat 28:63–105, 2008) showing new examples of Sasaki–Einstein 2-connected 7-manifolds homeomorphic to connected sums of <span>(S^3times S^4)</span>. Actually, we show that manifolds of the form <span>(#kleft( S^{3} times S^{4}right) )</span> admit Sasaki–Einstein metrics for 22 different values of <i>k</i>. All these links arise as Thom–Sebastiani sums of chain type singularities and cycle type singularities where Orlik’s conjecture holds due to a recent result by Hertling and Mase (J Algebra Number Theory 16(4):955–1024, 2022).</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796801","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
Berglund–Hübsch transpose rule and Sasakian geometry berglund - h<s:1> bsch转置定则与sasaki几何
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-11-16 DOI: 10.1007/s10455-023-09932-x
Ralph R. Gomez
{"title":"Berglund–Hübsch transpose rule and Sasakian geometry","authors":"Ralph R. Gomez","doi":"10.1007/s10455-023-09932-x","DOIUrl":"10.1007/s10455-023-09932-x","url":null,"abstract":"<div><p>We apply the Berglund–Hübsch transpose rule from BHK mirror symmetry to show that to an <span>(n-1)</span>-dimensional Calabi–Yau orbifold in weighted projective space defined by an invertible polynomial, we can associate four (possibly) distinct Sasaki manifolds of dimension <span>(2n+1)</span> which are <span>(n-1)</span>-connected and admit a metric of positive Ricci curvature. We apply this theorem to show that for a given K3 orbifold, there exist four seven-dimensional Sasakian manifolds of positive Ricci curvature, two of which are actually Sasaki–Einstein.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796802","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: 1
Boundary properties for a Monge-Ampère equation of prescribed affine Gauss curvature 给定仿射高斯曲率的monge - ampantere方程的边界性质
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-11-16 DOI: 10.1007/s10455-023-09933-w
Yadong Wu
{"title":"Boundary properties for a Monge-Ampère equation of prescribed affine Gauss curvature","authors":"Yadong Wu","doi":"10.1007/s10455-023-09933-w","DOIUrl":"10.1007/s10455-023-09933-w","url":null,"abstract":"<div><p>Considering a Monge-Ampère equation with prescribed affine Gauss curvature, we first show the completeness of centroaffine metric on the convex domain and derive a gradient estimate of the convex solution and then give different orders of two eigenvalues of the Hessian with respect to the distance function. We also show that the curvature of level sets of the convex solution is uniformly bounded, and show that there exist a class of Euclidean-complete hyperbolic surfaces with prescribed affine Gauss curvature and with bounded affine principal curvatures.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796803","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 metric structure of compact rank-one ECS manifolds 紧致1阶ECS流形的度量结构
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-10-26 DOI: 10.1007/s10455-023-09929-6
Andrzej Derdzinski, Ivo Terek
{"title":"The metric structure of compact rank-one ECS manifolds","authors":"Andrzej Derdzinski,&nbsp;Ivo Terek","doi":"10.1007/s10455-023-09929-6","DOIUrl":"10.1007/s10455-023-09929-6","url":null,"abstract":"<div><p>Pseudo-Riemannian manifolds with nonzero parallel Weyl tensor which are not locally symmetric are known as ECS manifolds. Every ECS manifold carries a distinguished null parallel distribution <span>(mathcal {D})</span>, the rank <span>(din {1,2})</span> of which is referred to as the rank of the manifold itself. Under a natural genericity assumption on the Weyl tensor, we fully describe the universal coverings of compact rank-one ECS manifolds. We then show that any generic compact rank-one ECS manifold must be <i>translational</i>, in the sense that the holonomy group of the natural flat connection induced on <span>(mathcal {D})</span> is either trivial or isomorphic to <span>({mathbb {Z}}_2)</span>. We also prove that all four-dimensional rank-one ECS manifolds are noncompact, this time without having to assume genericity, as it is always the case in dimension four.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"64 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09929-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134797739","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: 3
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