Pseudo generalized quasi-Einstein warped products manifolds with respect to affine connections

Resumo

In this paper, we investigate warped products on pseudo-generalized quasi-Einstein manifolds under affine connections. We explore their fundamental properties, establish conditions for their existence, and prove that these manifolds can be nearly quasi-Einstein and pseudo quasi-Einstein. To illustrate, we provide examples in Riemannian and Lorentzian geometries, confirming their existence. Finally, we construct and analyze an explicit example of a warped product on a pseudo-generalized quasi-Einstein manifold with respect to affine connections.