## Statistics and Probability African Society Editions

### Chapter 16. The Riemann extension of an affine Osserman connection on 3-dimensional manifold

Abdoul Salam DIALLO

#### Abstract

The Riemannian extension of torsion free affine manifolds $(M, \nabla)$ is an important method to produce pseudo-Riemannian manifolds. It is known that, if the manifold $(M, \nabla)$ is a torsion-free affine two-dimensional manifold with skew symmetric tensor Ricci, then $(M, \nabla)$ 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.

#### Chapter information

Source
Hamet Seydi, Gane Samb Lo, Aboubakary Diakhaby, eds., A Collection of Papers in Mathematics and Related Sciences, a Festschrift in Honour of the Late Galaye Dia, (Calgary, Alberta, 2018), 283-293

Dates
First available in Project Euclid: 26 September 2019