IJPAM: Volume 93, No. 4 (2014)

ON SUBMANIFOLDS OF A RIEMANNIAN MANIFOLD WITH
A SEMI-SYMMETRIC RECURRENT-METRIC CONNECTION

Jaeman Kim
Department of Mathematics Education
Kangwon National University
Chunchon 200-701, Kangwon Do, KOREA


Abstract. We study some properties of submanifolds of a Riemannian manifold with a semi-symmetric recurrent-metric connection. Among others, the Gauss equation, the Codazzi-Mainardi equation and the Ricci equation for such a connection have been derived.

Received: February 3, 2014

AMS Subject Classification: 53A30, 53B35, 53C25, 53C55, 53C56

Key Words and Phrases: submanifolds, semi-symmetric recurrent-metric connection, curvature with respect to semi-symmetric recurrent-metric connection, Gauss equation, Codazzi-Mainardi equation, Ricci equation, totally geodesic, totally umbilical, minimal, sectional curvature with respect to semi-symmetric recurrent-metric connection

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DOI: 10.12732/ijpam.v93i4.7 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 93
Issue: 4
Pages: 567 - 580

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).