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Open AccessArticle

A Characterization of Ruled Real Hypersurfaces in Non-Flat Complex Space Forms

1
Faculty of Mathematics and Engineering Sciences, Hellenic Army Academy, Vari, 16673 Attiki, Greece
2
Department of Mathematics, School of Sciences, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
3
Departmento de Geometria y Topologia, Universidad de Granada, 18071 Granada, Spain
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(4), 642; https://doi.org/10.3390/math8040642
Received: 28 March 2020 / Revised: 16 April 2020 / Accepted: 17 April 2020 / Published: 21 April 2020
(This article belongs to the Special Issue Differential Geometry: Theory and Applications)
The Levi-Civita connection and the k-th generalized Tanaka-Webster connection are defined on a real hypersurface M in a non-flat complex space form. For any nonnull constant k and any vector field X tangent to M the k-th Cho operator F X ( k ) is defined and is related to both connections. If X belongs to the maximal holomorphic distribution D on M, the corresponding operator does not depend on k and is denoted by F X and called Cho operator. In this paper, real hypersurfaces in non-flat space forms such that F X S = S F X , where S denotes the Ricci tensor of M and a further condition is satisfied, are classified. View Full-Text
Keywords: k-th generalized Tanaka-Webster connection; k-th Cho operator; real hypersurface; Ricci tensor; non-flat complex space form k-th generalized Tanaka-Webster connection; k-th Cho operator; real hypersurface; Ricci tensor; non-flat complex space form
MDPI and ACS Style

Kaimakamis, G.; Panagiotidou, K.; Pérez, J.D. A Characterization of Ruled Real Hypersurfaces in Non-Flat Complex Space Forms. Mathematics 2020, 8, 642.

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