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Some remarks on almost Hermitian functionals 关于几乎赫尔墨斯函数的一些评论
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-01-31 DOI: 10.1007/s10455-023-09943-8
Tedi Draghici, Cem Sayar
{"title":"Some remarks on almost Hermitian functionals","authors":"Tedi Draghici,&nbsp;Cem Sayar","doi":"10.1007/s10455-023-09943-8","DOIUrl":"10.1007/s10455-023-09943-8","url":null,"abstract":"<div><p>We study critical points of natural functionals on various spaces of almost Hermitian structures on a compact manifold <span>(M^{2n})</span>. We present a general framework, introducing the notion of gradient of an almost Hermitian functional. As a consequence of the diffeomorphism invariance, we show that a Schur’s type theorem still holds for general almost Hermitian functionals, generalizing a known fact for Riemannian functionals. We present two concrete examples, the Gauduchon’s functional and a close relative of it. These functionals have been studied previously, but not in the most general setup as we do here, and we make some new observations about their critical points.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139647779","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 subelliptic harmonic maps with potential 关于有潜力的亚椭圆谐波映射
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-01-30 DOI: 10.1007/s10455-023-09942-9
Yuxin Dong, Han Luo, Weike Yu
{"title":"On subelliptic harmonic maps with potential","authors":"Yuxin Dong,&nbsp;Han Luo,&nbsp;Weike Yu","doi":"10.1007/s10455-023-09942-9","DOIUrl":"10.1007/s10455-023-09942-9","url":null,"abstract":"<div><p>Let <span>((M,H,g_H;g))</span> be a sub-Riemannian manifold and (<i>N</i>, <i>h</i>) be a Riemannian manifold. For a smooth map <span>(u: M rightarrow N)</span>, we consider the energy functional <span>(E_G(u) = frac{1}{2} int _M[|textrm{d}u_text {H}|^2 - 2,G(u)] textrm{d}V_M)</span>, where <span>(textrm{d}u_text {H})</span> is the horizontal differential of <i>u</i>, <span>(G:Nrightarrow mathbb {R})</span> is a smooth function on <i>N</i>. The critical maps of <span>(E_G(u))</span> are referred to as subelliptic harmonic maps with potential <i>G</i>. In this paper, we investigate the existence problem for subelliptic harmonic maps with potentials by a subelliptic heat flow. Assuming that the target Riemannian manifold has nonpositive sectional curvature and the potential <i>G</i> satisfies various suitable conditions, we prove some Eells–Sampson-type existence results when the source manifold is either a step-2 sub-Riemannian manifold or a step-<i>r</i> sub-Riemannian manifold whose sub-Riemannian structure comes from a tense Riemannian foliation.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139648081","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
Almost CR manifolds with contracting CR automorphism 几乎 CR 流形的收缩 CR 自定态
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-01-23 DOI: 10.1007/s10455-023-09941-w
Jae-Cheon Joo, Kang-Hyurk Lee
{"title":"Almost CR manifolds with contracting CR automorphism","authors":"Jae-Cheon Joo,&nbsp;Kang-Hyurk Lee","doi":"10.1007/s10455-023-09941-w","DOIUrl":"10.1007/s10455-023-09941-w","url":null,"abstract":"<div><p>In this paper, we deal with a strongly pseudoconvex almost CR manifold with a CR contraction. We will prove that the stable manifold of the CR contraction is CR equivalent to the Heisenberg group model.\u0000</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139556531","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
Instability of a family of examples of harmonic maps 谐波映射实例族的不稳定性
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-01-09 DOI: 10.1007/s10455-023-09936-7
Nobumitsu Nakauchi
{"title":"Instability of a family of examples of harmonic maps","authors":"Nobumitsu Nakauchi","doi":"10.1007/s10455-023-09936-7","DOIUrl":"10.1007/s10455-023-09936-7","url":null,"abstract":"<div><p>The radial map <i>u</i>(<i>x</i>) <span>(=)</span> <span>(frac{x}{Vert xVert })</span> is a well-known example of a harmonic map from <span>({mathbb {R}}^m,-,{0})</span> into the spheres <span>({mathbb {S}}^{m-1})</span> with a point singularity at <i>x</i> <span>(=)</span> 0. In Nakauchi (Examples Counterexamples 3:100107, 2023), the author constructed recursively a family of harmonic maps <span>(u^{(n)})</span> into <span>({mathbb {S}}^{m^n-1})</span> with a point singularity at the origin <span>((n = 1,,2,ldots ))</span>, such that <span>(u^{(1)})</span> is the above radial map. It is known that for <i>m</i> <span>(ge )</span> 3, the radial map <span>(u^{(1)})</span> is not only <i>stable</i> as a harmonic map but also a <i>minimizer</i> of the energy of harmonic maps. In this paper, we show that for <i>n</i> <span>(ge )</span> 2, <span>(u^{(n)})</span> may be <i>unstable</i> as a harmonic map. Indeed we prove that under the assumption <i>n</i> &gt; <span>({displaystyle frac{sqrt{3}-1}{2},(m-1)})</span> <span>((m ge 3)</span>, <span>(n ge 2))</span>, the map <span>(u^{(n)})</span> is <i>unstable</i> as a harmonic map. It is remarkable that they are unstable and our result gives many examples of <i>unstable</i> harmonic maps into the spheres with a point singularity at the origin.\u0000</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139410564","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
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
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