Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2015; 52(5): 1621-1630

Printed September 30, 2015

https://doi.org/10.4134/BKMS.2015.52.5.1621

Copyright © The Korean Mathematical Society.

On the Lie derivative of Real Hypersurfaces in $\mathbb{C}P^{2}$ and $\mathbb{C}H^{2}$ with respect to the Generalized Tanaka-Webster connection

Konstantina Panagiotidou and Juan de Dios P\'erez

Aristotle University of Thessaloniki, Universidad de Granada

Abstract

In this paper the notion of Lie derivative of a tensor field $T$ of type (1,1) of real hypersurfaces in complex space forms with respect to the generalized Tanaka-Webster connection is introduced and is called \emph{generalized Tanaka-Webster Lie derivative}. Furthermore, three dimensional real hypersurfaces in non-flat complex space forms whose generalized Tanaka-Webster Lie derivative of 1) shape operator, 2) structure Jacobi operator coincides with the covariant derivative of them with respect to any vector field $X$ orthogonal to $\xi$ are studied.

Keywords: real hypersurface, structure Jacobi operator, shape operator, Lie derivative, generalized Tanaka-Webster connection

MSC numbers: Primary 53C40; Secondary 53C15, 53D15