On compact Einstein doubly warped product manifolds

Punam Gupta

Abstract


In this paper, the non-existence of connected, compact Einstein doubly warped product semi-Riemannian manifold with non-positive scalar curvature is proved. It is also shown that there does not exist non-trivial connected Einstein doubly warped product semi-Riemannian manifold with compact base $B$ or fibre $F$.

Keywords


Doubly warped product manifold; compact manifold; Einstein manifold

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DOI: http://dx.doi.org/10.5556/j.tkjm.49.2018.2605

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