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CHARACTERIZATIONS OF REAL HYPERSURFACES OF COMPLEX SPACE FORMS IN TERMS OF RICCI OPERATORS

  • Sohn, Woon-Ha (Department of Mathematics Hankuk University of Foreign Studies)
  • Published : 2007.02.28

Abstract

We prove that a real hypersurface M in a complex space form Mn(c), $c{\neq}0$, whose Ricci operator and structure tensor commute each other on the holomorphic distribution and the Ricci operator is ${\eta}-parallel$, is a Hopf hypersurface. We also give a characterization of this hypersurface.

Keywords

real hypersurfaces in complex space forms;Hopf hypersurfaces;model spaces of type A or B

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Cited by

  1. The Ricci Operator and Shape Operator of Real Hypersurfaces in a Non-Flat 2-Dimensional Complex Space Form vol.03, pp.02, 2013, https://doi.org/10.4236/apm.2013.32036
  2. A study of real hypersurfaces with Ricci operators in 2-dimensional complex space forms vol.266, pp.2, 2013, https://doi.org/10.2140/pjm.2013.266.305