ON THE LIE DERIVATIVE OF REAL HYPERSURFACES IN ℂP^{2} AND ℂH^{2} WITH RESPECT TO THE GENERALIZED TANAKA-WEBSTER CONNECTION

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 52, Issue 5, 2015, pp.1621-1630
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2015.52.5.1621

Title & Authors

ON THE LIE DERIVATIVE OF REAL HYPERSURFACES IN ℂP^{2} AND ℂH^{2} WITH RESPECT TO THE GENERALIZED TANAKA-WEBSTER CONNECTION

PANAGIOTIDOU, KONSTANTINA; PEREZ, JUAN DE DIOS;

PANAGIOTIDOU, KONSTANTINA; PEREZ, JUAN DE DIOS;

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 are studied.

Keywords

real hypersurface;structure Jacobi operator;shape operator;Lie derivative;generalized Tanaka-Webster connection;

Language

English

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