CHARACTERIZATIONS OF REAL HYPERSURFACES OF TYPE A IN A COMPLEX SPACE FORM

Title & Authors
CHARACTERIZATIONS OF REAL HYPERSURFACES OF TYPE A IN A COMPLEX SPACE FORM
Ki, U-Hang; Kim, In-Bae; Lim, Dong-Ho;

Abstract
Let M be a real hypersurface with almost contact metric structure $\small{(\phi,g,\xi,\eta)}$ in a complex space form $\small{M_n(c)}$, $\small{c\neq0}$. In this paper we prove that if $\small{R_{\xi}L_{\xi}g=0}$ holds on M, then M is a Hopf hypersurface in $\small{M_n(c)}$, where $\small{R_{\xi}}$ and $\small{L_{\xi}}$ denote the structure Jacobi operator and the operator of the Lie derivative with respect to the structure vector field $\small{\xi}$ respectively. We characterize such Hopf hypersurfaces of $\small{M_n(c)}$.
Keywords
real hypersurface;structure Jacobi operator;Hopf hypersurface;
Language
English
Cited by
1.
On characterizations of real hypersurface in complex space form with Codazzi type structure Lie operator, Monatshefte für Mathematik, 2014, 173, 3, 371
2.
On Characterizations of Hopf Hypersurfaces in a Nonflat Complex Space Form with Anti-commuting Operators, Results in Mathematics, 2017, 71, 1-2, 197
3.
Real hypersurfaces with Killing type operators in a nonflat complex space form, Journal of Geometry, 2017
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