On the Ricci curvature of submanifolds in the warped product $L \times_{f} F $

Young-Mi Kim; Jin Suk Pak

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J. Korean Math. Soc. 2002; 39(5): 693-708

Printed September 1, 2002

On the Ricci curvature of submanifolds in the warped product $L \times_{f} F $

Young-Mi Kim and Jin Suk Pak

Kyungpook National University

Abstract

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Abstract

The warped product $L \times_{f} F $ of a line $L$ and a Kaehler manifold $F$ is a typical example of Kenmotsu manifold. In this paper we determine submanifolds of $L \times_{f} F$ which are tangent to the structure vector field and satisfy certain conditions concerning with Ricci curvature and mean curvature.

Keywords: Kenmotsu manifold, totally real submanifold, Ricci curvature

MSC numbers: 53B40