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# A Classification of Three-dimensional Real Hypersurfaces in Non-flat Complex Space Forms in Terms of Their generalized Tanaka-Webster Lie Derivative

Published:2016-08-19
Printed: Dec 2016
• George Kaimakamis,
Faculty of Mathematics and Engineering Sciences, Hellenic Military Academy, Vari, Attiki, Greece
• Konstantina Panagiotidou,
Faculty of Mathematics and Engineering Sciences, Hellenic Military Academy, Vari, Attiki, Greece
• Juan de Dios Pérez,
On a real hypersurface $M$ in a non-flat complex space form there exist the Levi-Civita and the k-th generalized Tanaka-Webster connections. The aim of the present paper is to study three dimensional real hypersurfaces in non-flat complex space forms, whose Lie derivative of the structure Jacobi operator with respect to the Levi-Civita connections coincides with the Lie derivative of it with respect to the k-th generalized Tanaka-Webster connection. The Lie derivatives are considered in direction of the structure vector field and in directions of any vecro field orthogonal to the structure vector field.
 Keywords: $k$-th generalized Tanaka-Webster connection, non-flat complex space form, real hypersurface, Lie derivative, structure Jacobi operator