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Warped products with Tripathi connections

  • Abdoul Salam DialloEmail author
  • Fortuné Massamba
  • Salomon Joseph Mbatakou
Article
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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 \(M_2\).

Keywords

Warped product Levi-Civita connection Tripathi connection Semi-symmetric connection Quarter-symmetric connection 

Mathematics Subject Classification

53B05 53B15 53B20 

Notes

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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Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2019

Authors and Affiliations

  • Abdoul Salam Diallo
    • 1
    • 2
    Email author
  • Fortuné Massamba
    • 1
  • Salomon Joseph Mbatakou
    • 1
  1. 1.School of Mathematics, Statistics and Computer ScienceUniversity of KwaZulu-NatalPietermaritzburgSouth Africa
  2. 2.Département de MathématiquesUniversité Alioune Diop de Bambey, UFR SaticBambeySenegal

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