Statistics and Probability African Society Editions
Chapter 16. The Riemann extension of an affine Osserman connection on 3-dimensional manifold
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.
First available in Project Euclid: 26 September 2019
Permanent link to this document
Digital Object Identifier
DIALLO, Abdoul Salam. Chapter 16. The Riemann extension of an affine Osserman connection on 3-dimensional manifold. A Collection of Papers in Mathematics and Related Sciences, 283--293, Statistics and Probability African Society, Calgary, Alberta, 2018. doi:10.16929/sbs/2018.100-03-04. https://projecteuclid.org/euclid.spaseds/1569509476