Statistics and Probability African Society Editions

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

Abdoul Salam DIALLO

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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

Permanent link to this document
https://projecteuclid.org/euclid.spaseds/1569509476

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

Subjects
Primary: 53B05: Linear and affine connections 53B20: Local Riemannian geometry 53C30: Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]

Keywords
affine connection Jacobi operator Osserman manifold Riemann extension

Citation

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


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