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On Lorentzian Spaces of Constant Sectional Curvature

Vladica Andrejić

Faculty of Mathematics, University of Belgrade, Belgrade, Serbia

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 Rakić 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.

Keywords: Lorentzian space, Osserman manifold, duality principle

Classification (MSC2000): 53B30; 53C50

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Electronic fulltext finalized on: 26 Apr 2018. This page was last modified: 11 Mai 2018.

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