TANGENT BUNDLES ENDOWED WITH SEMI-SYMMETRIC NON-METRIC CONNECTION ON A RIEMANNIAN MANIFOLD

Mohammad Nazrul Islam Khan

DOI Number
https://doi.org/10.22190/FUMI210111064K
First page
855
Last page
878

Abstract


The differential geometry of the tangent bundle is an effective domain of differential geometry which reveals many new problems in the study of modern differential geometry. The generalization of connection on any manifold to its tangent bundle is an application of differential geometry. Recently a new type of semi-symmetric non-metric connection on a Riemannian manifold is studied and established a relationship between Levi-Civita connection and semi-symmetric non-metric connection. The various properties of a Riemannian manifold with relation to such connection are also discussed. The present paper aims to study the tangent bundle of a new type of semi-symmetric non-metric connection on a Riemannian manifold. The necessary and sufficient conditions for projectively invariant curvature tensors corresponding to such connection are proved and show many basic results on the Riemannian manifold in the tangent bundle. Furthermore, the properties of group manifolds of the Riemannian manifolds with respect to the semi-symmetric non-metric connection in the tangent bundle are studied.
Moreover, theorems on the symmetry property of Ricci tensor and Ricci soliton in the tangent bundle are established.


Keywords

Tangent bundle, Vertical and complete lifts, Riemannian manifold, semi-symmetric non-metric connection, Different curvature tensors.

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DOI: https://doi.org/10.22190/FUMI210111064K

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