A note on some generalized curvature tensor

Abstract

For any semi-Riemannian manifold (M,g) we define some generalized curvature tensor as a linear combination of Kulkarni-Nomizu products formed by the metric tensor, the Ricci tensor and its square of given manifold. That tensor is closely related to quasi-Einstein spaces, Roter spaces and some Roter type spaces.

arXiv admin note: substantial text overlap with arXiv:2211.06700, arXiv:1911.02482, arXiv:1810.01402