Quasi-Einstein manifolds with structure of warped product product
Abstract
In this paper we prove that under certain conditions in a quasi Einstein semi Riemannian warped product the fiber is necessarily a Einstein manifold. We provide all the quasi Einstein manifolds when r Bakry Emery tensor is null, the base is conformal to an n-dimensional pseudo-Euclidean space invariant under the action of an n - 1 dimensional translation group and the fiber is Ricci flat. As an application, we have built a family of Ricci flat Einstein warped product whose base is not locally conformally flat.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2019
- DOI:
- 10.48550/arXiv.1905.02006
- arXiv:
- arXiv:1905.02006
- Bibcode:
- 2019arXiv190502006G
- Keywords:
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- Mathematics - Differential Geometry;
- 53C21 53C50 53C25
- E-Print:
- arXiv admin note: text overlap with arXiv:1505.03833