Derivatives of the Operator ϕA-Aϕ on a Real Hypersurface in Non-flat Complex Space Forms

On a real hypersurface M in a non-flat complex space form, two types of connections can be defined: the Levi-Civita connection, which is torsion free and, for any nonnull constant k , the k th generalized Tanaka-Webster connection, which is an affine connection with torsion. So the associated covari...

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Bibliographic Details
Published in:Bulletin of the Malaysian Mathematical Sciences Society 2020, Vol.43 (1), p.267-282
Main Authors: Kaimakamis, George, Panagiotidou, Konstantina, Pérez, Juan de Dios
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
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Summary:On a real hypersurface M in a non-flat complex space form, two types of connections can be defined: the Levi-Civita connection, which is torsion free and, for any nonnull constant k , the k th generalized Tanaka-Webster connection, which is an affine connection with torsion. So the associated covariant derivatives can be considered. Moreover, the Lie derivative and a derivative of Lie type associated with the k th generalized Tanaka-Webster connection can be defined. In this paper, real hypersurfaces for which both covariant derivatives or Lie derivative and the derivative of Lie type associated with the k th generalized Tanaka-Webster connection coincide when they act on the operator ϕ A - A ϕ , where ϕ denotes the structure operator and A the shape operator of M , either in the direction of the structure vector field ξ or in any direction of the maximal holomorphic distribution of M are classified.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-018-0679-9