On Warped Product Manifolds Satisfying Ricci–Hessian Class Type Equations

Sinem Güler, Sezgin Altay Demirbağ

Abstract: We deal with a study of warped product manifold which is also a generalized quasi Einstein manifold. Then, we investigate the relationships between such warped products and certain manifolds that provide some Ricci–Hessian type equations, such as ${Ric}_f^m=\lambda g$ for some smooth function $\lambda$, where ${Ric}_f^m$ denotes the $m$-Bakery–Emery Ricci tensor. Finally, we obtain some rigidity conditions for such manifolds.

Keywords: $m$-Bakery–Emery Ricci tensor, generalized quasi Einstein manifold, warped product manifold, conformal vector field

Classification (MSC2000): 53C15; 53C25,53B15

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