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2010•Honam Mathematical JournalOpen access

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

Mobin Ahmad, Jae-Bok Jun

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Abstract

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

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

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Available abstract

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

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

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