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http://dx.doi.org/10.4134/BKMS.2015.52.5.1621

ON THE LIE DERIVATIVE OF REAL HYPERSURFACES IN ℂP2 AND ℂH2 WITH RESPECT TO THE GENERALIZED TANAKA-WEBSTER CONNECTION  

PANAGIOTIDOU, KONSTANTINA (FACULTY OF ENGENEERING ARISTOTLE UNIVERSITY OF THESSALONIKI)
PEREZ, JUAN DE DIOS (DEPARTMENTO DE GEOMETRIA Y TOPOLOGIA UNIVERSIDAD DE GRANADA)
Publication Information
Bulletin of the Korean Mathematical Society / v.52, no.5, 2015 , pp. 1621-1630 More about this Journal
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 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;
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