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2011•Journal of the Chungcheong Mathematical SocietyRequires access

SUBMANIFOLDS OF AN ALMOST $r$ -PARACONTACT RIEMANNIAN MANIFOLD ENDOWED WITH A QUARTER-SYMMETRIC NON-METRIC CONNECTION

Mobin Ahmad, Jae-Bok Jun, Abdul Haseeb

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Abstract

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

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

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Available abstract

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

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

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