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has been cited by the following article:

• TITLE: Commuting Structure Jacobi Operator for Real Hypersurfaces in Complex Space Forms

  AUTHORS: U-Hang Ki, Hiroyuki Kurihara

  KEYWORDS: Complex Space Form; Hopf Hypersurface; Structure Jacobi Operator; Shape Operator; Ricci Tensor

  JOURNAL NAME: Advances in Pure Mathematics, Vol.3 No.2, March 14, 2013

  ABSTRACT: Let M be a real hypersurface of a complex space form with almost contact metric structure (φ,ξ,η,g). In this paper, we prove that if the structure Jacobi operator Rξ=(·,ξ) ξ is φ▽ξξ-parallel and Rξ commute with the shape operator, then M is a Hopf hypersurface. Further, if Rξ is φ▽ξξ-parallel and Rξ commute with the Ricci tensor, then M is also a Hopf hypersurface provided that TrRξ is constant.