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Onreal hypersurfaces of a complex projective space with recurrent Riccitensor

Published online by Cambridge University Press:  01 October 1999

Tatsuyoshi Hamada
Tatsuyoshi Hamada
Affiliation:
Department of Applied Mathematics, Fukuoka University, Fukuoka, 814-0180, Japan. E-mail:hamada@sm.fukuoka-u.ac.jp
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Abstract

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Let M be a real hypersurface of the complex projective space Pn(C). The Ricci tensor S of M is recurrent if there exists a 1-form $\alpha$ such that $\nablaS=S\otimes\alpha;$. In this paper we show that there are no real hypersurfaces with recurrent Ricci tensor of Pn(C) under the condition that $\xi$ is a principal curvature vector.

1991 Mathematics Subject Classification 53C40 (53C25).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 41 , Issue 3 , October 1999 , pp. 297 - 302
Copyright
1999 Glasgow Mathematical Journal Trust