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 \(M_2\).
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Acknowledgements
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).
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Diallo, A.S., Massamba, F. & Mbatakou, S.J. Warped products with Tripathi connections. Afr. Mat. 30, 389–398 (2019). https://doi.org/10.1007/s13370-019-00655-6
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DOI: https://doi.org/10.1007/s13370-019-00655-6
Keywords
- Warped product
- Levi-Civita connection
- Tripathi connection
- Semi-symmetric connection
- Quarter-symmetric connection