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# On Characterizations of Real Hypersurfaces in a Complex Space Form with $\eta$-Parallel Shape Operator

Published:2011-03-10
Printed: Mar 2012
• S. H. Kon,
Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia.
• Tee-How Loo,
Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia.
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## Abstract

In this paper we study real hypersurfaces in a non-flat complex space form with $\eta$-parallel shape operator. Several partial characterizations of these real hypersurfaces are obtained.
 Keywords: complex space form, Hopf hypersurfaces, ruled real hypersurfaces, $\eta$-parallel shape operator
 MSC Classifications: 53C40 - Global submanifolds [See also 53B25] 53C15 - General geometric structures on manifolds (almost complex, almost product structures, etc.)