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The super-Sasaki metric on the antitangent bundle 反切束上的超级佐佐木度规
arXiv: Differential Geometry Pub Date : 2020-01-24 DOI: 10.1142/S0219887820501224
A. Bruce
{"title":"The super-Sasaki metric on the antitangent bundle","authors":"A. Bruce","doi":"10.1142/S0219887820501224","DOIUrl":"https://doi.org/10.1142/S0219887820501224","url":null,"abstract":"We show how to lift a Riemannian metric and almost symplectic form on a manifold to a Riemannian structure on a canonically associated supermanifold known as the antitangent or shifted tangent bundle. We view this construction as a generalisation of Sasaki's construction of a Riemannian metric on the tangent bundle of a Riemannian manifold.","PeriodicalId":8430,"journal":{"name":"arXiv: Differential Geometry","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78700466","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Expected distances on manifolds of partially oriented flags 部分定向标志的流形上的期望距离
arXiv: Differential Geometry Pub Date : 2020-01-22 DOI: 10.1090/proc/15521
Brenden Balch, C. Peterson, C. Shonkwiler
{"title":"Expected distances on manifolds of partially oriented flags","authors":"Brenden Balch, C. Peterson, C. Shonkwiler","doi":"10.1090/proc/15521","DOIUrl":"https://doi.org/10.1090/proc/15521","url":null,"abstract":"Flag manifolds are generalizations of projective spaces and other Grassmannians: they parametrize flags, which are nested sequences of subspaces in a given vector space. These are important objects in algebraic and differential geometry, but are also increasingly being used in data science, where many types of data are properly understood as subspaces rather than vectors. In this paper we discuss partially oriented flag manifolds, which parametrize flags in which some of the subspaces may be endowed with an orientation. We compute the expected distance between random points on some low-dimensional examples, which we view as a statistical baseline against which to compare the distances between particular partially oriented flags coming from geometry or data.","PeriodicalId":8430,"journal":{"name":"arXiv: Differential Geometry","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84633937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
On the stability of compact pseudo-Kähler and neutral Calabi-Yau manifolds 紧致pseudo-Kähler和中性Calabi-Yau流形的稳定性
arXiv: Differential Geometry Pub Date : 2020-01-14 DOI: 10.1016/J.MATPUR.2020.09.001
A. Latorre, L. Ugarte
{"title":"On the stability of compact pseudo-Kähler and neutral Calabi-Yau manifolds","authors":"A. Latorre, L. Ugarte","doi":"10.1016/J.MATPUR.2020.09.001","DOIUrl":"https://doi.org/10.1016/J.MATPUR.2020.09.001","url":null,"abstract":"","PeriodicalId":8430,"journal":{"name":"arXiv: Differential Geometry","volume":"92 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83777647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Direct sum for basic cohomology of codimension four taut Riemannian foliation 余维四紧黎曼叶理的基本上同调的直接和
arXiv: Differential Geometry Pub Date : 2020-01-08 DOI: 10.4134/BKMS.B200022
Jiuru Zhou
{"title":"Direct sum for basic cohomology of codimension four taut Riemannian foliation","authors":"Jiuru Zhou","doi":"10.4134/BKMS.B200022","DOIUrl":"https://doi.org/10.4134/BKMS.B200022","url":null,"abstract":"We discuss the decomposition of degree two basic cohomology for codimension four taut Riemannian foliation according to the holonomy invariant transversal almost complex structure J, and show that J is C pure and full. In addition, we obtain an estimate of the dimension of basic J-anti-invariant subgroup. These are the foliated version for the corresponding results of T. Draghici et al.","PeriodicalId":8430,"journal":{"name":"arXiv: Differential Geometry","volume":"60 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72910835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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 Maximal Rate of Convergence Under the Ricci Flow 关于Ricci流下的最大收敛速率
arXiv: Differential Geometry Pub Date : 2020-01-05 DOI: 10.1093/imrn/rnaa172
Brett L. Kotschwar
{"title":"On the Maximal Rate of Convergence Under the Ricci Flow","authors":"Brett L. Kotschwar","doi":"10.1093/imrn/rnaa172","DOIUrl":"https://doi.org/10.1093/imrn/rnaa172","url":null,"abstract":"We estimate from above the rate at which a solution to the normalized Ricci flow on a closed manifold may converge to a limit soliton. Our main result implies that any solution which converges modulo diffeomorphisms to a soliton faster than any fixed exponential rate must itself be self-similar.","PeriodicalId":8430,"journal":{"name":"arXiv: Differential Geometry","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74277215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Constructions of Compact $$G_2$$-Holonomy Manifolds 紧的构造$$G_2$$ -完整流形
arXiv: Differential Geometry Pub Date : 2020-01-01 DOI: 10.1007/978-1-0716-0577-6_2
A. Kovalev
{"title":"Constructions of Compact $$G_2$$-Holonomy Manifolds","authors":"A. Kovalev","doi":"10.1007/978-1-0716-0577-6_2","DOIUrl":"https://doi.org/10.1007/978-1-0716-0577-6_2","url":null,"abstract":"","PeriodicalId":8430,"journal":{"name":"arXiv: Differential Geometry","volume":"20 1","pages":"51-67"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84391589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Distinguished $$G_2$$-Structures on Solvmanifolds Distinguished $$G_2$$ - solvmanifold上的结构
arXiv: Differential Geometry Pub Date : 2020-01-01 DOI: 10.1007/978-1-0716-0577-6_9
J. Lauret
{"title":"Distinguished $$G_2$$-Structures on Solvmanifolds","authors":"J. Lauret","doi":"10.1007/978-1-0716-0577-6_9","DOIUrl":"https://doi.org/10.1007/978-1-0716-0577-6_9","url":null,"abstract":"","PeriodicalId":8430,"journal":{"name":"arXiv: Differential Geometry","volume":"36 1","pages":"217-233"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77247448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Nil-Killing vector fields and type III deformations 零杀伤向量场和III型变形
arXiv: Differential Geometry Pub Date : 2019-12-05 DOI: 10.1063/5.0018773
M. Aadne
{"title":"Nil-Killing vector fields and type III deformations","authors":"M. Aadne","doi":"10.1063/5.0018773","DOIUrl":"https://doi.org/10.1063/5.0018773","url":null,"abstract":"This paper is concerned with deformations of Kundt metrics in the direction of type $III$ tensors and nil-Killing vector fields whose flows give rise to such deformations. We find various characterizations within the Kundt class in terms of nil-Killing vector fields and obtain a theorem classifying algebraic stability of tensors, which has an application in finding sufficient criteria for a type $III$ deformation of the metric to preserve spi's. This is used in order to specify Lie algebras of nil-Killing vector fields that preserve the spi's, for degenerate Kundt metrics. Using this we discuss the characterization of Kundt-CSI spacetimes in terms of nil-Killing vector fields.","PeriodicalId":8430,"journal":{"name":"arXiv: Differential Geometry","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89435643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
The $W$-curvature tensor on relativistic space-times 相对论时空上的W曲率张量
arXiv: Differential Geometry Pub Date : 2019-12-01 DOI: 10.5666/KMJ.2020.60.1.185
H. Abu-Donia, S. Shenawy, A. Syied
{"title":"The $W$-curvature tensor on relativistic space-times","authors":"H. Abu-Donia, S. Shenawy, A. Syied","doi":"10.5666/KMJ.2020.60.1.185","DOIUrl":"https://doi.org/10.5666/KMJ.2020.60.1.185","url":null,"abstract":"This paper aims to study the $W$-curvature tensor on relativistic space-times. The energy-momentum tensor T of a space-time is semi-symmetric given that the $W$-curvature tensor is semi-symmetric whereas energy-momentum tensor T of a space-time having a divergence free $W$-curvature tensor is of Codazzi type. A space-time having a traceless $W$-curvature tensor is Einstein. A $W$-curvature flat space-time is Einstein. Perfect fluid space-times which admits $W$-curvature tensor are considered.","PeriodicalId":8430,"journal":{"name":"arXiv: Differential Geometry","volume":"99 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75931243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Spectra of compact quotients of the oscillator group 振子群紧商的谱
arXiv: Differential Geometry Pub Date : 2019-11-29 DOI: 10.3842/SIGMA.2021.051
Mathias Fischer, I. Kath
{"title":"Spectra of compact quotients of the oscillator group","authors":"Mathias Fischer, I. Kath","doi":"10.3842/SIGMA.2021.051","DOIUrl":"https://doi.org/10.3842/SIGMA.2021.051","url":null,"abstract":"We consider the oscillator group ${rm Osc}_1$, which is a semi-direct product of the three-dimensional Heisenberg group and the real line. We classify the lattices of ${rm Osc}_1$ up to inner automorphisms of ${rm Osc}_1$. For every lattice $L$ in ${rm Osc}_1$, we compute the decomposition of the right regular representation of ${rm Osc}_1$ on $L^2(Lbackslash{rm Osc}_1)$ into irreducible unitary representations. This decomposition is called the spectrum of the quotient $Lbackslash{rm Osc}_1$.","PeriodicalId":8430,"journal":{"name":"arXiv: Differential Geometry","volume":"63 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86031421","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
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