On doubly warped products

Year 2020, Volume: 69 Issue: 2, 1329 - 1335, 31.12.2020

Sibel Gerdan Aydın , Hakan Mete Taştan

https://doi.org/10.31801/cfsuasmas.635048

Cited By: 3

https://izlik.org/JA83LU98XA

Abstract

We give a new characterization for doubly warped products by using the geometry of their canonical foliations intersecting perpendicularly. We also give a necessary and sufficient condition for a doubly warped product to be a warped or a direct product. As a result, we prove the non-existence of Einstein proper doubly warped product pseudo-Riemannian manifold of dimension grater or equal than 4.                                                                                                    .

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Keywords

Doubly warped product , warped product , direct product , Einstein manifold

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