Warped products with Tripathi connections
- 2 Downloads
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 \(M_2\).
KeywordsWarped product Levi-Civita connection Tripathi connection Semi-symmetric connection Quarter-symmetric connection
Mathematics Subject Classification53B05 53B15 53B20
The first and third authors also express their deepest gratitude to the University of KwaZulu-Natal for support and hospitality. This work is based on the research supported in part by the National Research Foundation of South Africa (Grant numbers 95931 and 106072).