On some Quasi-Einstein and 2-Quasi-Einstein manifolds

On some Quasi-Einstein and 2-Quasi-Einstein manifolds

R Deszcz, M Głogowska, M Hotloś, Z Şentürk – AIP Conference Proceedings, 2022

The tensor R· C− C· R and the tensors Q (g, R), Q (S, R), Q (g, C) and Q (S, C) of every Einstein manifold (M, g), n≥ 4, satisfy R· C− C· R=(κ/((n− 1) n)) Q (g, R)=(κ/((n−1) n)) Q (g, C)=(1/(n− 1)) Q (S, R)=(1/(n− 1)) Q (S, C). Motivated by this we study curvature properties of non-Einstein and non-conformally flat semi-Riemannian manifolds of dimension≥ 4 satisfying the following family of generalized Einstein metric conditions: the tensor R· C− C· R is a linear combination of the tensors Q (g …

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