IJPAM: Volume 104, No. 4 (2015)

ON SUBMANIFOLDS OF
GENERALIZED RECURRENT MANIFOLDS

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


Abstract. In this paper we investigate some properties of submanifolds of generalized recurrent manifold (briefly, $GRM_{n}$). Firstly, we show that a totally geodesic hypersurface of $GRM_{n}$ is a $GRM_{n-1}$. Secondly, if $GRM_{n}$ is a Riemannian product manifold, then either one decomposition manifold is locally symmetric or the other decomposition manifold is a space of constant curvature. Thirdly, a Riemannian product manifold of a space of constant curvature with itself is a $GRM_{n}$.

Received: July 22, 2015

AMS Subject Classification: 53A55, 53B20

Key Words and Phrases: totally umbilic hypersurface, totally geodesic hypersurface, generalized recurrent manifold, Riemannian product manifold, associated 1-forms, a space of constant curvature

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DOI: 10.12732/ijpam.v104i4.9 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: 2015
Volume: 104
Issue: 4
Pages: 577 - 584


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