Open Access
VOL. 1 | 2018 Chapter 16. The Riemann extension of an affine Osserman connection on 3-dimensional manifold
Chapter Author(s) Abdoul Salam DIALLO
Editor(s) Hamet SEYDI, Gane Samb LO, Aboubakary DIAKHABY

Abstract

The Riemannian extension of torsion free affine manifolds (M,) is an important method to produce pseudo-Riemannian manifolds. It is known that, if the manifold (M,) is a torsion-free affine two-dimensional manifold with skew symmetric tensor Ricci, then (M,) is affine Osserman manifold. In higher dimensions the skew symmetric of the tensor Ricci is a necessary but not sufficient condition for a affine connection to be Osserman. In this paper we construct affine Osserman connection with Ricci flat but not flat and example of Osserman pseudo-Riemannian metric of signature (3,3) is exhibited.

Information

Published: 1 January 2018
First available in Project Euclid: 26 September 2019

Digital Object Identifier: 10.16929/sbs/2018.100-03-04

Subjects:
Primary: 53B05 , 53B20 , 53C30

Keywords: affine connection , Jacobi operator , Osserman manifold , Riemann extension

Rights: Copyright © 2018 The Statistics and Probability African Society

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