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

  • Received : 2014.10.30
  • Published : 2015.09.30

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.

Acknowledgement

Supported by : National Research Foundation of Korea

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  1. Comparison of Differential Operators with Lie Derivative of Three-Dimensional Real Hypersurfaces in Non-Flat Complex Space Forms vol.6, pp.5, 2018, https://doi.org/10.3390/math6050084