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Generalized complex structure on certain principal torus bundles 若干主环面束上的广义复结构
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-12-09 DOI: 10.1007/s10455-024-09982-9
Debjit Pal, Mainak Poddar
{"title":"Generalized complex structure on certain principal torus bundles","authors":"Debjit Pal,&nbsp;Mainak Poddar","doi":"10.1007/s10455-024-09982-9","DOIUrl":"10.1007/s10455-024-09982-9","url":null,"abstract":"<div><p>A principal torus bundle over a complex manifold with even dimensional fiber and characteristic class of type (1, 1) admits a family of regular generalized complex structures (GCS) with the fibers as leaves of the associated symplectic foliation. We show that such a generalized complex structure is equivalent to the product of the complex structure on the base and the symplectic structure on the fiber in a tubular neighborhood of an arbitrary fiber if and only if the bundle is flat. This has consequences for the generalized Dolbeault cohomology of the bundle that includes a Künneth formula. On a more general note, if a principal bundle over a complex manifold with a symplectic structure group admits a GCS with the fibers of the bundle as leaves of the associated symplectic foliation, and the GCS is equivalent to a product GCS in a neighborhood of every fiber, then the bundle is flat and symplectic.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"67 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142798443","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
Coclosed (G_2)-structures on (text {SU}(2)^2)-invariant cohomogeneity one manifolds 在(text {SU}(2)^2)-invariant cohomogeneity one流形上的茧（G_2）-结构
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-11-26 DOI: 10.1007/s10455-024-09981-w
Izar Alonso
{"title":"Coclosed (G_2)-structures on (text {SU}(2)^2)-invariant cohomogeneity one manifolds","authors":"Izar Alonso","doi":"10.1007/s10455-024-09981-w","DOIUrl":"10.1007/s10455-024-09981-w","url":null,"abstract":"<div><p>We consider two different <span>(text {SU}(2)^2)</span>-invariant cohomogeneity one manifolds, one non-compact <span>(M=mathbb {R}^4 times S^3)</span> and one compact <span>(M=S^4 times S^3)</span>, and study the existence of coclosed <span>(text {SU}(2)^2)</span>-invariant <span>(G_2)</span>-structures constructed from half-flat <span>(text {SU}(3))</span>-structures. For <span>(mathbb {R}^4 times S^3)</span>, we prove the existence of a family of coclosed (but not necessarily torsion-free) <span>(G_2)</span>-structures which is given by three smooth functions satisfying certain boundary conditions around the singular orbit and a non-zero parameter. Moreover, any coclosed <span>(G_2)</span>-structure constructed from a half-flat <span>(text {SU}(3))</span>-structure is in this family. For <span>(S^4 times S^3)</span>, we prove that there are no <span>(text {SU}(2)^2)</span>-invariant coclosed <span>(G_2)</span>-structures constructed from half-flat <span>(text {SU}(3))</span>-structures.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"67 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-024-09981-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714428","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
Generalized positive scalar curvature on spin(^c) manifolds 自旋（^c）流形上的广义正标量曲率
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-11-01 DOI: 10.1007/s10455-024-09977-6
Boris Botvinnik, Jonathan Rosenberg
{"title":"Generalized positive scalar curvature on spin(^c) manifolds","authors":"Boris Botvinnik,&nbsp;Jonathan Rosenberg","doi":"10.1007/s10455-024-09977-6","DOIUrl":"10.1007/s10455-024-09977-6","url":null,"abstract":"<div><p>Let (<i>M</i>, <i>L</i>) be a (compact) non-spin spin<span>(^c)</span> manifold. Fix a Riemannian metric <i>g</i> on <i>M</i> and a connection <i>A</i> on <i>L</i>, and let <span>(D_L)</span> be the associated spin<span>(^c)</span> Dirac operator. Let <span>(R^{text {tw }}_{(g,A)}:=R_g + 2ic(Omega ))</span> be the <i>twisted scalar curvature</i> (which takes values in the endomorphisms of the spinor bundle), where <span>(R_g)</span> is the scalar curvature of <i>g</i> and <span>(2ic(Omega ))</span> comes from the curvature 2-form <span>(Omega )</span> of the connection <i>A</i>. Then the Lichnerowicz-Schrödinger formula for the square of the Dirac operator takes the form <span>(D_L^2 =nabla ^*nabla + frac{1}{4}R^{text {tw }}_{(g,A)})</span>. In a previous work we proved that a closed non-spin simply-connected spin<span>(^c)</span>-manifold (<i>M</i>, <i>L</i>) of dimension <span>(nge 5)</span> admits a pair (<i>g</i>, <i>A</i>) such that <span>(R^{text {tw }}_{(g,A)}&gt;0)</span> if and only if the index <span>(alpha ^c(M,L):={text {ind}}D_L)</span> vanishes in <span>(K_n)</span>. In this paper we introduce a scalar-valued <i>generalized scalar curvature</i> <span>(R^{text {gen }}_{(g,A)}:=R_g - 2|Omega |_{op})</span>, where <span>(|Omega |_{op})</span> is the pointwise operator norm of Clifford multiplication <span>(c(Omega ))</span>, acting on spinors. We show that the positivity condition on the operator <span>(R^{text {tw }}_{(g,A)})</span> is equivalent to the positivity of the scalar function <span>(R^{text {gen }}_{(g,A)})</span>. We prove a corresponding trichotomy theorem concerning the curvature <span>(R^{text {gen }}_{(g,A)})</span>, and study its implications. We also show that the space <span>(mathcal {R}^{{textrm{gen}+}}(M,L))</span> of pairs (<i>g</i>, <i>A</i>) with <span>(R^{text {gen }}_{(g,A)}&gt;0)</span> has non-trivial topology, and address a conjecture about non-triviality of the “index difference” map.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"66 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142565893","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 zeta-determinant of the Dirichlet-to-Neumann operator on forms 形式上的狄利克特到诺伊曼算子的zeta决定子
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-10-07 DOI: 10.1007/s10455-024-09975-8
Klaus Kirsten, Yoonweon Lee
{"title":"The zeta-determinant of the Dirichlet-to-Neumann operator on forms","authors":"Klaus Kirsten,&nbsp;Yoonweon Lee","doi":"10.1007/s10455-024-09975-8","DOIUrl":"10.1007/s10455-024-09975-8","url":null,"abstract":"<div><p>On a compact Riemannian manifold <i>M</i> with boundary <i>Y</i>, we express the log of the zeta-determinant of the Dirichlet-to-Neumann operator acting on <i>q</i>-forms on <i>Y</i> as the difference of the log of the zeta-determinant of the Laplacian on <i>q</i>-forms on <i>M</i> with the absolute boundary condition and that of the Laplacian with the Dirichlet boundary condition with an additional term which is expressed by curvature tensors. When the dimension of <i>M</i> is 2 and 3, we compute these terms explicitly. We also discuss the value of the zeta function at zero associated to the Dirichlet-to-Neumann operator by using a metric rescaling method. As an application, we recover the result of the conformal invariance obtained in Guillarmou and Guillope (Int Math Res Not IMRN 2007(22):rnm099, 2007) when <span>({text {dim}}M = 2)</span>.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"66 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142410453","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
A critical perturbation result in prescribing scalar curvature under boundary conditions 边界条件下规定标量曲率的临界扰动结果
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-10-07 DOI: 10.1007/s10455-024-09976-7
Azeb Alghanemi, Aymen Bensouf, Hichem Chtioui
{"title":"A critical perturbation result in prescribing scalar curvature under boundary conditions","authors":"Azeb Alghanemi,&nbsp;Aymen Bensouf,&nbsp;Hichem Chtioui","doi":"10.1007/s10455-024-09976-7","DOIUrl":"10.1007/s10455-024-09976-7","url":null,"abstract":"<div><p>We consider the problem of finding conformal metrics on the standard half sphere with prescribed scalar curvature and zero-boundary mean curvature. We prove a perturbation result when the curvature function is flat near its boundary critical points. As a product we extend some previous well known results and provide an entirely new one.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"66 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142410452","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 the Gromov–Hausdorff limits of compact surfaces with boundary 关于有边界的紧凑曲面的格罗莫夫-豪斯多夫极限
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-10-01 DOI: 10.1007/s10455-024-09973-w
Tobias Dott
{"title":"On the Gromov–Hausdorff limits of compact surfaces with boundary","authors":"Tobias Dott","doi":"10.1007/s10455-024-09973-w","DOIUrl":"10.1007/s10455-024-09973-w","url":null,"abstract":"<div><p>In this work we investigate Gromov–Hausdorff limits of compact surfaces carrying length metrics. More precisely, we consider the case where all surfaces have the same Euler characteristic. We give a complete description of the limit spaces and study their topological properties. Our investigation builds on the results of a previous work which treats the case of closed surfaces.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"66 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-024-09973-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409301","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
Frölicher spectral sequence of compact complex manifolds with special Hermitian metrics 具有特殊赫米特度量的紧凑复流形的福禄克谱序列
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-10-01 DOI: 10.1007/s10455-024-09972-x
Adela Latorre, Luis Ugarte, Raquel Villacampa
{"title":"Frölicher spectral sequence of compact complex manifolds with special Hermitian metrics","authors":"Adela Latorre,&nbsp;Luis Ugarte,&nbsp;Raquel Villacampa","doi":"10.1007/s10455-024-09972-x","DOIUrl":"10.1007/s10455-024-09972-x","url":null,"abstract":"<div><p>In this paper we focus on the interplay between the behaviour of the Frölicher spectral sequence and the existence of special Hermitian metrics on the manifold, such as balanced, SKT or generalized Gauduchon. The study of balanced metrics on nilmanifolds endowed with strongly non-nilpotent complex structures allows us to provide infinite families of compact balanced manifolds with Frölicher spectral sequence not degenerating at the second page. Moreover, this result is extended to non-degeneration at any arbitrary page. Similar results are obtained for the Frölicher spectral sequence of compact generalized Gauduchon manifolds. We also find a compact SKT manifold whose Frölicher spectral sequence does not degenerate at the second page, thus providing a counterexample to a conjecture by Popovici.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"66 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-024-09972-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409364","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
Compact minimal submanifolds of the Riemannian symmetric spaces ({{textbf {S}}U}(n)/textbf{SO}(n)), ({{textbf {S}}p}(n)/{{textbf {U}}}(n)), (textbf{SO}(2n)/{{textbf {U}}}(n)), ({{textbf {S}}U}(2n)/{{textbf {S}}p}(n)) via complex-valued eigenfunctions Riemannian 对称空间的紧凑最小子漫游空间 （{textbf {S}U}(n)/textbf{SO}(n)), （{textbf {S}p}(n)/{textbf {U}}(n))、通过复值特征函数，(textbf{SO}(2n)/{{textbf {U}}(n)), ({{textbf {S}}U}(2n)/{{textbf {S}}p}(n))
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-09-27 DOI: 10.1007/s10455-024-09974-9
Johanna Marie Gegenfurtner, Sigmundur Gudmundsson
{"title":"Compact minimal submanifolds of the Riemannian symmetric spaces ({{textbf {S}}U}(n)/textbf{SO}(n)), ({{textbf {S}}p}(n)/{{textbf {U}}}(n)), (textbf{SO}(2n)/{{textbf {U}}}(n)), ({{textbf {S}}U}(2n)/{{textbf {S}}p}(n)) via complex-valued eigenfunctions","authors":"Johanna Marie Gegenfurtner,&nbsp;Sigmundur Gudmundsson","doi":"10.1007/s10455-024-09974-9","DOIUrl":"10.1007/s10455-024-09974-9","url":null,"abstract":"<div><p>In this work we construct new multi-dimensional families of compact minimal submanifolds of the classical Riemannian symmetric spaces <span>({{textbf {S}}U}(n)/textbf{SO}(n))</span>, <span>({{textbf {S}}p}(n)/{{textbf {U}}}(n))</span>, <span>(textbf{SO}(2n)/{{textbf {U}}}(n))</span> and <span>({{textbf {S}}U}(2n)/{{textbf {S}}p}(n))</span> of codimension two.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"66 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-024-09974-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142414509","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
Heat-type equations on manifolds with fibered boundaries I: Schauder estimates 有纤维边界流形上的热型方程 I：绍德估计
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-09-26 DOI: 10.1007/s10455-024-09970-z
Bruno Caldeira, Giuseppe Gentile
{"title":"Heat-type equations on manifolds with fibered boundaries I: Schauder estimates","authors":"Bruno Caldeira,&nbsp;Giuseppe Gentile","doi":"10.1007/s10455-024-09970-z","DOIUrl":"10.1007/s10455-024-09970-z","url":null,"abstract":"<div><p>In this paper, we prove parabolic Schauder estimates for the Laplace-Beltrami operator on a manifold <i>M</i> with fibered boundary and a <span>(Phi )</span>-metric <span>(g_Phi )</span>. This setting generalizes the asymptotically conical (scattering) spaces and includes special cases of gravitational instantons. This paper, combined with part II, lay the crucial groundwork for forthcoming discussions on geometric flows in this setting; especially the Yamabe- and mean curvature flow.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"66 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413911","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
Estimates of Kähler metrics on noncompact finite volume hyperbolic Riemann surfaces, and their symmetric products 非紧凑有限体积双曲黎曼曲面上的凯勒度量及其对称积的估算
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-09-25 DOI: 10.1007/s10455-024-09967-8
Anilatmaja Aryasomayajula, Arijit Mukherjee
{"title":"Estimates of Kähler metrics on noncompact finite volume hyperbolic Riemann surfaces, and their symmetric products","authors":"Anilatmaja Aryasomayajula,&nbsp;Arijit Mukherjee","doi":"10.1007/s10455-024-09967-8","DOIUrl":"10.1007/s10455-024-09967-8","url":null,"abstract":"<div><p>Let <i>X</i> denote a noncompact finite volume hyperbolic Riemann surface of genus <span>(gge 2)</span>, with only one puncture at <span>(iinfty )</span> (identifying <i>X</i> with its universal cover <span>({mathbb {H}})</span>). Let <span>({{{overline{X}}}}:=Xcup lbrace iinfty rbrace )</span> denote the Satake compactification of <i>X</i>. Let <span>(Omega _{{{{overline{X}}}}})</span> denote the cotangent bundle on <span>({{{overline{X}}}})</span>. For <span>(kgg 1)</span>, we derive an estimate for <span>(mu _{{ {overline{X}}}}^{textrm{Ber},{{k}}})</span>, the Bergman metric associated to the line bundle <span>({{mathcal {L}}}^{k}:=Omega _{{{{overline{X}}}}}^{otimes {{k}}}otimes {{mathcal {O}}}_{{{{overline{X}}}}}((k-1)iinfty ))</span>. For a given <span>(dge 1)</span>, the pull-back of the Fubini-Study metric on the Grassmannian, which we denote by <span>(mu _{textrm{Sym}^{{d}}({{overline{X}}})}^{textrm{FS},k})</span>, defines a Kähler metric on <span>(textrm{Sym}^{{d}}({{overline{X}}}))</span>, the <i>d</i>-fold symmetric product of <span>({{{overline{X}}}})</span>. Using our estimates of <span>(mu _{{ {overline{X}}}}^{textrm{Ber},{{k}}})</span>, as an application, we derive an estimate for <span>(mu _{textrm{Sym}^{{d}}({{overline{X}}}),textrm{vol}}^{textrm{FS},k})</span>, the volume form associated to the (1,1)-form <span>(mu _{textrm{Sym}^{{d}}({{overline{X}}})}^{textrm{FS},k})</span>.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"66 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413790","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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