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
Bull. Korean Math. Soc. 2015 Vol. 52, No. 5, 1621-1630
https://doi.org/10.4134/BKMS.2015.52.5.1621
Printed September 30, 2015
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
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