On the duality principle in pseudo-Riemannian Osserman manifolds

被引：12

作者：

Andrejic, V. ^{[1
]}

Rakic, Z. ^{[1
]}

机构：

[1] Univ Belgrade, Fac Math, Belgrade 11001, Serbia

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2007年 / 57卷 / 10期

关键词：

pseudo-Riemannian manifold; Jacobi operator; pointwise Osserman manifold; Osserman algebraic curvature tensor; duality principle;

D O I：

10.1016/j.geomphys.2007.06.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Here we give a natural extension of the duality principle for the curvature tensor of pointwise pseudo-Riemannian Osserman manifolds. We proved that this extended duality principle holds under certain additional assumptions. Also, it is proved that duality principle holds for every four-dimensional Osserman manifold. (c) 2007 Elsevier B.V. All rights reserved.

引用

页码：2158 / 2166

页数：9

共 50 条

[1] Nonsymmetric Osserman pseudo-Riemannian manifolds
Garcia-Rio, E
Vazquez-Abal, ME
Vazquez-Lorenzo, R
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 126 (09) : 2771 - 2778
[2] Szabo Osserman IP pseudo-riemannian manifolds
Gilkey, PB
Ivanova, R
Zhang, T
PUBLICATIONES MATHEMATICAE-DEBRECEN, 2003, 62 (3-4): : 387 - 401
[3] Higher-order Jordan Osserman pseudo-Riemannian manifolds
Gilkey, PB
Ivanova, R
Zhang, T
CLASSICAL AND QUANTUM GRAVITY, 2002, 19 (17) : 4543 - 4551
[4] Curvature homogeneous spacelike Jordan Osserman pseudo-Riemannian manifolds
Gilkey, P
Nikcevic, S
CLASSICAL AND QUANTUM GRAVITY, 2004, 21 (02) : 497 - 507
[5] Osserman pseudo-Riemannian manifolds of signature (2,2)
Blazic, N
Bokan, N
Rakic, Z
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 2001, 71 : 367 - 395
[6] On duality principle in Osserman manifolds
Rakic, Z
LINEAR ALGEBRA AND ITS APPLICATIONS, 1999, 296 (1-3) : 183 - 189
[7] On duality principle in Osserman manifolds
Rakic, Zoran
Linear Algebra and Its Applications, 296 (01): : 183 - 189
[8] Pseudo-Riemannian manifolds
Girbau J.
Bruna L.
Progress in Mathematical Physics, 2010, 58 : 1 - 17
[9] DUALITY PRINCIPLE AND SPECIAL OSSERMAN MANIFOLDS
Andrejic, Vladica
PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD, 2013, 94 (108): : 197 - 204
[10] Higher order Osserman pseudo-Riemannian manifolds of neutral signature (2,2)
Sterbeti, Catalin
BALKAN JOURNAL OF GEOMETRY AND ITS APPLICATIONS, 2005, 10 (01): : 175 - 178

← 1 2 3 4 5 →