Vol. 266, No. 2, 2013

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A study of real hypersurfaces with Ricci operators in 2-dimensional complex space forms

Dong Ho Lim, Woon Ha Sohn and Hyunjung Song

Vol. 266 (2013), No. 2, 305–311
Abstract

We prove that a real hypersurface M in complex projective space P2() or complex hyperbolic space H2(), whose Ricci operator is η-parallel and commutes with the structure tensor on the holomorphic distribution, is a Hopf hypersurface. We also give a characterization of this hypersurface.

Keywords
real hypersurface, η-parallel Ricci operator, Hopf hypersurface
Mathematical Subject Classification 2010
Primary: 53C40
Secondary: 53C15
Milestones
Received: 20 September 2012
Revised: 6 May 2013
Accepted: 13 June 2013
Published: 12 November 2013
Authors
Dong Ho Lim
Department of Mathematics
Hankuk University of Foreign Studies
Seoul 130-791
South Korea
Woon Ha Sohn
Department of Mathematics
Catholic University of Daegu
Daegu 712-702
South Korea
Hyunjung Song
Department of Mathematics
Hankuk University of Foreign Studies
Seoul 130-791
South Korea