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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
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- Journal:
- Canadian Mathematical Bulletin / Volume 59 / Issue 4 / 01 December 2016
- Published online by Cambridge University Press:
- 20 November 2018, pp. 813-823
- Print publication:
- 01 December 2016
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- Article
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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 this paper is to study three dimensional real hypersurfaces in non-flat complex space forms, whose Lie derivative of the structure Jacobi operatorwith respect to the Levi–Civita connection 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 direction of any vector field orthogonal to the structure vector field.
