On doubly warped products

Authors : Sibel GERDAN AYDIN, Hakan Mete TAŞTAN

Pages : 1329-1335

Doi:10.31801/cfsuasmas.635048

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Publication Date : 2020-12-31

Article Type : Research Paper

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.                                                                                                    . .
Keywords : Doubly warped product, warped product, direct product, Einstein manifold