Kodai Mathematical Journal

The structure Jacobi operator of three-dimensional real hypersurfaces in non-flat complex space forms

George Kaimakamis, Konstantina Panagiotidou, and Juan de Dios Pérez

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Abstract

In this paper new results concerning three dimensional real hypersurfaces in non-flat complex space forms in terms of their stucture Jacobi operator are presented. More precisely, the conditions of 1) the structure Jacobi operator being of Codazzi type with respect to the generalized Tanaka-Webster connection and commuting with the shape operator and 2) η-invariance of the structure Jacobi operator and commutativity of it with the shape operator are studied. Furthermore, results concerning Hopf hypersurfaces and ruled hypersurfaces of dimension greater than three satisfying the previous conditions are also included.

Article information

Source
Kodai Math. J., Volume 39, Number 1 (2016), 154-174.

Dates
First available in Project Euclid: 22 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1458651697

Digital Object Identifier
doi:10.2996/kmj/1458651697

Mathematical Reviews number (MathSciNet)
MR3478276

Zentralblatt MATH identifier
1344.53042

Citation

Kaimakamis, George; Panagiotidou, Konstantina; Pérez, Juan de Dios. The structure Jacobi operator of three-dimensional real hypersurfaces in non-flat complex space forms. Kodai Math. J. 39 (2016), no. 1, 154--174. doi:10.2996/kmj/1458651697. https://projecteuclid.org/euclid.kmj/1458651697


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