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SUBMANIFOLDS OF AN ALMOST r-PARACONTACT RIEMANNIAN MANIFOLD ENDOWED WITH SEMI-SYMMETRIC SEMI-METRIC CONNECTION

Mobin Ahmad, Jae-Bok Jun, Abdul Haseeb

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Abstract

We define a quarter symmetric metric connection in an almost − r paracontact Riemannian manifold and we consider submanifolds of an almost − r paracontact Riemannian manifold endowed with a quarter symmetric metric connection. We also obtain Gauss and Codazzi equations, Weingarten equation and curvature tensor for submanifolds of an almost − r paracontact Riemannian manifold

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What this paper is about

We define a quarter symmetric metric connection in an almost − r paracontact Riemannian manifold and we consider submanifolds of an almost − r paracontact Riemannian manifold endowed with a quarter symmetric metric connection. We also obtain Gauss and Codazzi equations, Weingarten equation and curvature tensor for submanifolds of an almost − r paracontact Riemannian manifold

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Available abstract

We define a quarter symmetric metric connection in an almost − r paracontact Riemannian manifold and we consider submanifolds of an almost − r paracontact Riemannian manifold endowed with a quarter symmetric metric connection. We also obtain Gauss and Codazzi equations, Weingarten equation and curvature tensor for submanifolds of an almost − r paracontact Riemannian manifold

Key concepts: Mathematics, Connection (principal bundle), Pseudo-Riemannian manifold, Riemannian manifold, Ricci curvature, Levi-Civita connection, Fundamental theorem of Riemannian geometry, Metric connection

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SUBMANIFOLDS OF AN ALMOST r-PARACONTACT RIEMANNIAN MANIFOLD ENDOWED WITH SEMI-SYMMETRIC SEMI-METRIC CONNECTION — Research Paper | ScholarLens