# Warped products with a Tripathi connection

## TL;DR

This paper investigates warped product manifolds equipped with a Tripathi connection, establishing relationships between the connections on the product and its factors, contributing to differential geometry and physics applications.

## Contribution

It introduces and analyzes the properties of Tripathi connections on warped product manifolds, a novel extension in the study of such geometric structures.

## Key findings

- Relationships between Tripathi connections on the warped product and its factors.
- Characterization of geometric properties under Tripathi connection.
- Potential applications in physics and differential geometry.

## 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 $M_2$.