Curvature properties of pseudosymmetry type of some 2-quasi-Einstein manifolds

TL;DR

This paper investigates the curvature properties of 2-quasi-Einstein semi-Riemannian manifolds, establishing conditions under which certain pseudosymmetry types are satisfied, with applications to specific warped product manifolds and spacetimes.

Contribution

It proves that 2-quasi-Einstein manifolds with a specific curvature tensor structure satisfy pseudosymmetry conditions, extending understanding of their geometric properties.

Findings

Certain 2-quasi-Einstein manifolds satisfy pseudosymmetry conditions.

Warped product manifolds with 2-dimensional base are examples.

Some spacetimes are shown to be 2-quasi-Einstein with these properties.

Abstract

Let (M,g) be a 2-quasi-Einstein non-conformally flat semi-Riemannian manifold of dimension > 3. We prove that if its Riemann-Christoffel curvature tensor R is a linear combination of some Kulkarni-Nomizu tensors formed by the metric tensor g, the Ricci tensor S and its square S^2, then some pseudosymmetry type curvature conditions are satisfied. Certain non-conformally flat warped product manifolds with 2-dimensional base, and in particular some spacetimes, are such 2-quasi Einstein manifolds.