Geometric properties of submanifolds of a Riemannian manifold in tangent bundles
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Keywords:
Tangent bundle,, Mathematical operators, Induced metric, Connection, Gauss equation, Weingarten equation, Codazzi equation, Curvature tensor, Hypersurface, SubmanifoldAbstract
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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