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The structure vector field and structure Jacobi operator of real hypersurfaces in nonflat complex space forms

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Abstract

In this paper we determine the real hypersurfaces for which the structure Jacobi operator commutes over both the Ricci tensors and structure tensors (for a definition of the operator see Sect. 1). We prove that such hypersurfaces are homogneous real hypersurfaces of type (A) and are a special class of Hopf hypersurfaces.

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Authors and Affiliations

  1. Department of Mathematics, Kyungpook National University, Daegu, 702-701, Korea

    U-Hang Ki

  2. Department of Mathematics, University of Toyama, 3190 Gofuku, Toyamashi, 930-8555, Japan

    Setsuo Nagai

  3. Department of Mathematics and Informatics, Chiba University, Chibashi, 263-8522, Japan

    Ryoichi Takagi

Authors
  1. U-Hang Ki
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  2. Setsuo Nagai
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  3. Ryoichi Takagi
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Corresponding author

Correspondence to Setsuo Nagai.

Additional information

Partially supported by Grant-in-aid for Scientific Research No. 19540070.

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Ki, UH., Nagai, S. & Takagi, R. The structure vector field and structure Jacobi operator of real hypersurfaces in nonflat complex space forms. Geom Dedicata 149, 161–176 (2010). https://doi.org/10.1007/s10711-010-9474-y

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  • DOI: https://doi.org/10.1007/s10711-010-9474-y

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