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On Warped Product Manifolds Satisfying Ricci–Hessian Class Type Equations

Sinem Güler, Sezgin Altay Demirbağ

Department of Mathematics, Istanbul Technical University, 34469 Maslak, Istanbul, Turkey

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 =λg for some smooth function λ, 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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Electronic fulltext finalized on: 26 Apr 2018. This page was last modified: 11 Mai 2018.

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