Warped products with a Tripathi connection

Abdoul Salam Diallo; Fortuné Massamba; Salomon Joseph Mbatakou

paper

Warped products with a Tripathi connection

arXiv:1703.08507

Abstract

The warped product $M_{1} \times_{F} M_{2}$ of two Riemannian manifolds $(M_{1}, g_{1})$ and $(M_{2}, g_{2})$ is the product manifold $M_{1} \times M_{2}$ equipped with the warped product metric $g = g_{1} + F^{2} g_{2}$ , where $F$ is a positive function on $M_{1}$ . The notion of warped product manifolds is one of the most fruitful generalizations of Riemannian products. Such a notion plays very important roles in differential geometry as well as in physics, especially in general relativity. In this paper we study warped product manifolds endowed with a Tripathi connection. We establish some relationships between the Tripathi connection of the warped product $M$ to those $M_{1}$ and $M_{2}$ .

13 pages