Cyclic $\eta$-parallel shape and Ricci operators on real hypersurfaces in two-dimensional nonflat complex space forms

Yaning Wang

Vol. 302 (2019), No. 1, 335–352

DOI: 10.2140/pjm.2019.302.335

Abstract

We consider three-dimensional real hypersurfaces in a nonflat complex space form of complex dimension two with cyclic $\eta$-parallel shape or Ricci operators and classify such hypersurfaces satisfying some other geometric restrictions. Some results extend those of Ahn et al. (1993), Lim et al. (2013), Kim et al. (2007) and Sohn (2007).

Keywords

real hypersurface, complex space forms, cyclic $\eta$-parallel, shape operator, Ricci operator

Mathematical Subject Classification 2010

Primary: 53B25, 53D15

Milestones

Received: 2 June 2018

Revised: 8 September 2018

Accepted: 15 February 2019

Published: 5 November 2019