On Lorentzian spaces of constant sectional curvature
-
Published:2018
Issue:117
Volume:103
Page:7-15
-
ISSN:0350-1302
-
Container-title:Publications de l'Institut Math?matique (Belgrade)
-
language:en
-
Short-container-title:Publ Inst Math (Belgr)
Affiliation:
1. Faculty of Mathematics, Belgrade
Abstract
We investigate Osserman-like conditions for Lorentzian curvature tensors that
imply constant sectional curvature. It is known that Osserman (moreover
zwei-stein) Lorentzian manifolds have constant sectional curvature. We prove
that some generalizations of the Rakic duality principle (Lorentzian totally
Jacobi-dual or four-dimensional Lorentzian Jacobi-dual) imply constant
sectional curvature. Moreover, any four-dimensional Jacobi-dual algebraic
curvature tensor such that the Jacobi operator for some nonnull vector is
diagonalizable, is Osserman. Additionally, any Lorentzian algebraic
curvature tensor such that the reduced Jacobi operator for all nonnull
vectors has a single eigenvalue has a constant sectional curvature.
Funder
Ministry of Education, Science and Technological Development of the Republic of Serbia
Publisher
National Library of Serbia
Subject
General Mathematics
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献