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

George Kaimakamis, Konstantina Panagiotidou and Juan de Dios Pérez
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George Kaimakamis: Faculty of Mathematics and Engineering Sciences, Hellenic Army Academy, Vari, 16673 Attiki, Greece
Konstantina Panagiotidou: Faculty of Mathematics and Engineering Sciences, Hellenic Army Academy, Vari, 16673 Attiki, Greece
Juan de Dios Pérez: Departmento de Geometria y Topologia, Universidad de Granada, 18071 Granada, Spain

Mathematics, 2020, vol. 8, issue 4, 1-12

Abstract: 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.

Keywords: k-th generalized Tanaka-Webster connection; k-th Cho operator; real hypersurface; Ricci tensor; non-flat complex space form (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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