Geometric properties of submanifolds of a Riemannian manifold in tangent bundles


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Authors

  • Mohammad Nazrul Islam Khan Qassim University
  • Nahid Fatima
  • Afifah Al Eid
  • B. B. Chaturvedi
  • Mohit Saxena

Keywords:

Tangent bundle,, Mathematical operators, Induced metric, Connection, Gauss equation, Weingarten equation, Codazzi equation, Curvature tensor, Hypersurface, Submanifold

Abstract

The authors consider a quarter-symmetric semi-metric connection
(QSSM) connection in the tangent bundle and study the connection on
submanifold of co-dimension 2 and hypersurface concerning the QSSM
connection in the tangent bundle. Totally geodesic (TG), totally umbilical (TU), Gauss, Weingarten and Codazzi equations concerning the QSSM connection on submanifold of co-dimension 2 and hypersurface in the tangent bundle are obtained. Finally, we deduce Riemannian curvature tensor, Gauss and Codazzi equations on a submanifold of codimension 2 and hypersurface of Riemannian manifold concerning the quarter symmetric semi-metric connection in the tangent bundle.

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Published

2024-06-03

How to Cite

Khan, M. N. I., Nahid Fatima, Al Eid, A., Chaturvedi, B. B., & Saxena, M. (2024). Geometric properties of submanifolds of a Riemannian manifold in tangent bundles. Results in Nonlinear Analysis, 7(2), 140–153. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/373