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

Author

Listed:
  • George Kaimakamis

    (Faculty of Mathematics and Engineering Sciences, Hellenic Army Academy, Vari, 16673 Attiki, Greece
    These authors contributed equally to this work.)

  • Konstantina Panagiotidou

    (Faculty of Mathematics and Engineering Sciences, Hellenic Army Academy, Vari, 16673 Attiki, Greece
    Department of Mathematics, School of Sciences, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
    These authors contributed equally to this work.)

  • Juan de Dios Pérez

    (Departmento de Geometria y Topologia, Universidad de Granada, 18071 Granada, Spain
    These authors contributed equally to this work.)

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.

Suggested Citation

  • George Kaimakamis & Konstantina Panagiotidou & Juan de Dios Pérez, 2020. "A Characterization of Ruled Real Hypersurfaces in Non-Flat Complex Space Forms," Mathematics, MDPI, vol. 8(4), pages 1-12, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:642-:d:348616
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