Share This Article:

Commuting Structure Jacobi Operator for Real Hypersurfaces in Complex Space Forms

Full-Text HTML XML Download Download as PDF (Size:241KB) PP. 264-276
DOI: 10.4236/apm.2013.32038    3,338 Downloads   5,622 Views Citations

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 φξξ-parallel and Rξ commute with the shape operator, then M is a Hopf hypersurface. Further, if Rξ is φξξ-parallel and Rξ commute with the Ricci tensor, then M is also a Hopf hypersurface provided that TrRξ is constant.

Cite this paper

U. Ki and H. Kurihara, "Commuting Structure Jacobi Operator for Real Hypersurfaces in Complex Space Forms," Advances in Pure Mathematics, Vol. 3 No. 2, 2013, pp. 264-276. doi: 10.4236/apm.2013.32038.

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.