  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 $M_2$.
