On pseudo-Riemannian manifolds whose Ricci tensor is parallel

被引：7

作者：

Boubel, C ^{[1
]}

Bergery, LB ^{[1
]}

机构：

[1] Univ Nancy 1, INRIA, Inst Eli Cartan, CNRS,Unite Mixte Rech 7502, F-54506 Vandoeuvre Les Nancy, France

来源：

GEOMETRIAE DEDICATA | 2001年 / 86卷 / 1-3期

关键词：

pseudo-Riemannian manifolds; Ricci curvature; holonomy group;

D O I：

10.1023/A:1011903507837

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Ricci-parallel Riemannian manifolds have a diagonal Ricci endomorphism Ric and are therefore, at least locally, a product of Einstein manifolds. This fails in the pseudo-Riemannian case. Using, on the one side, a general result in linear algebra due to Klingenberg and on the other side, a theorem on the holonomy of pseudo-Riemannian manifolds, this work classifies the different types of pseudo-Riemannian manifolds whose Ricci tensor is parallel.

引用

页码：1 / 18

页数：18

共 50 条

[1] On Pseudo-Riemannian Manifolds Whose Ricci Tensor is Parallel
Charles Boubel
Lionel Bérard Bergery
[J]. Geometriae Dedicata, 2001, 86 : 1 - 18
[2] Compact pseudo-Riemannian manifolds with parallel Weyl tensor
Derdzinski, Andrzej
Roter, Witold
[J]. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 2010, 37 (01) : 73 - 90
[3] Compact pseudo-Riemannian manifolds with parallel Weyl tensor
Andrzej Derdzinski
Witold Roter
[J]. Annals of Global Analysis and Geometry, 2010, 37 : 73 - 90
[4] Almost *-η-Ricci solitons on Kenmotsu pseudo-Riemannian manifolds
Rashmi, S. V. Divya
Venkatesha, V.
[J]. ANALYSIS-INTERNATIONAL MATHEMATICAL JOURNAL OF ANALYSIS AND ITS APPLICATIONS, 2022, 42 (04): : 241 - 250
[5] Parallel pure spinors on pseudo-Riemannian manifolds
Kath, I
[J]. GEOMETRY AND TOPOLOGY OF SUBMANIFOLDS X: DIFFERENTIAL GEOMETRY IN HONOR OF PROF S.S. CHERN, 2000, : 87 - 103
[6] Parallel spinors on pseudo-Riemannian spinc manifolds
Ikemakhen, Aziz
[J]. JOURNAL OF GEOMETRY AND PHYSICS, 2006, 56 (09) : 1473 - 1483
[7] A Comprehensive Survey on Parallel Submanifolds in Riemannian and Pseudo-Riemannian Manifolds
Chen, Bang-Yen
[J]. AXIOMS, 2019, 8 (04)
[8] Characterizations of Ricci–Bourguignon Almost Solitons on Pseudo-Riemannian Manifolds
Dhriti Sundar Patra
Akram Ali
Fatemah Mofarreh
[J]. Mediterranean Journal of Mathematics, 2022, 19
[9] On pseudo-Riemannian manifolds with recurrent concircular curvature tensor
Olszak, K.
Olszak, Z.
[J]. ACTA MATHEMATICA HUNGARICA, 2012, 137 (1-2) : 64 - 71
[10] On pseudo-Riemannian manifolds with recurrent concircular curvature tensor
Karina Olszak
Zbigniew Olszak
[J]. Acta Mathematica Hungarica, 2012, 137 : 64 - 71

← 1 2 3 4 5 →