JACOBI OPERATORS ALONG THE STRUCTURE FLOW ON REAL HYPERSURFACES IN A NONFLAT COMPLEX SPACE FORM II

Title & Authors
JACOBI OPERATORS ALONG THE STRUCTURE FLOW ON REAL HYPERSURFACES IN A NONFLAT COMPLEX SPACE FORM II
Ki, U-Hang; Kurihara, Hiroyuki;

Abstract
Let M be a real hypersurface of a complex space form with almost contact metric structure ($\small{{\phi}}$, $\small{{\xi}}$, $\small{{\eta}}$, g). In this paper, we study real hypersurfaces in a complex space form whose structure Jacobi operator $\small{R_{\xi}=R({\cdot},\;{\xi}){\xi}}$ is $\small{{\xi}}$-parallel. In particular, we prove that the condition $\small{{\nabla}_{\xi}R_{\xi}=0}$ characterizes the homogeneous real hypersurfaces of type A in a complex projective space or a complex hyperbolic space when $\small{R_{\xi}{\phi}S=R_{\xi}S{\phi}}$ holds on M, where S denotes the Ricci tensor of type (1,1) on M.
Keywords
complex space form;real hypersurface;structure Jacobi operator;Ricci tensor;
Language
English
Cited by
1.
REAL HYPERSURFACES OF NON-FLAT COMPLEX SPACE FORMS WITH GENERALIZED ξ-PARALLEL JACOBI STRUCTURE OPERATOR, Glasgow Mathematical Journal, 2016, 58, 03, 677
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