Prescribing Ricci curvature on homogeneous spaces

被引：6
|
作者：
Lauret, Jorge [1 ,2 ]
Will, Cynthia E. [1 ,2 ]
机构：
[1] Univ Nacl Cordoba, Cordoba, Argentina
[2] CIEM, CONICET, Cordoba, Argentina
来源：
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2022年 / 2022卷 / 783期
关键词：
METRICS; NONEXISTENCE;
D O I：
10.1515/crelle-2021-0069
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The prescribed Ricci curvature problem in the context of G-invariant metrics on a homogeneous space M = G/K is studied. We focus on the metrics at which the map g bar right arrow Rc(g) is, locally, as injective and surjective as it can be. Our main result is that such property is generic in the compact case. Our main tool is a formula for the Lichnerowicz Laplacian we prove in terms of the moment map for the variety of algebras.
引用
收藏
页码：95 / 133
页数：39
相关论文
共 50 条
  • [21] Homogeneous spaces, curvature and cohomology
    Herrmann, Martin
    DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2016, 48 : 1 - 10
  • [22] HOMOGENEOUS SPACES OF POSITIVE CURVATURE
    WALLACH, NR
    NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 19 (02): : A401 - A402
  • [23] On a Generalization of Curvature Homogeneous Spaces
    O. Kowalski
    A. Vanžurová
    Results in Mathematics, 2013, 63 : 129 - 134
  • [24] On a Generalization of Curvature Homogeneous Spaces
    Kowalski, O.
    Vanzurova, A.
    RESULTS IN MATHEMATICS, 2013, 63 (1-2) : 129 - 134
  • [25] Metrics of positive Ricci curvature on quotient spaces
    Lorenz J. Schwachhöfer
    Wilderich Tuschmann
    Mathematische Annalen, 2004, 330 : 59 - 91
  • [26] HYPERSURFACES OF RANDERS SPACES WITH POSITIVE RICCI CURVATURE
    Li, Jintang
    Luo, Miao
    COLLOQUIUM MATHEMATICUM, 2023, 172 (01) : 85 - 98
  • [27] Ricci curvature of Markov chains on metric spaces
    Ollivier, Yann
    JOURNAL OF FUNCTIONAL ANALYSIS, 2009, 256 (03) : 810 - 864
  • [28] On quotients of spaces with Ricci curvature bounded below
    Galaz-Garcia, Fernando
    Kell, Martin
    Mondino, Andrea
    Sosa, Gerardo
    JOURNAL OF FUNCTIONAL ANALYSIS, 2018, 275 (06) : 1368 - 1446
  • [29] STRATIFIED SPACES AND SYNTHETIC RICCI CURVATURE BOUNDS
    Bertrand, Jerome
    Ketterer, Christian
    Mondello, Ilaria
    Richard, Thomas
    ANNALES DE L INSTITUT FOURIER, 2021, 71 (01) : 123 - 173
  • [30] Ricci curvature on Alexandrov spaces and rigidity theorems
    Zhang, Hui-Chun
    Zhu, Xi-Ping
    COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2010, 18 (03) : 503 - 553
12345