We classify real hypersurfaces in complex two-plane Grassmannians whose structure Jacobi operator commutes either with any other Jacobi operator or with the normal Jacobi operator.
We prove the non-existence of Hopf real hypersurfaces in complex two-plane Grassmannians whose Jacobi operators or the Jacobi corresponding to the directions in the distribution are of Codazzi type if they satisfy a f...We prove the non-existence of Hopf real hypersurfaces in complex two-plane Grassmannians whose Jacobi operators or the Jacobi corresponding to the directions in the distribution are of Codazzi type if they satisfy a further condition. We obtain that that they must be either of type (A) or of type (B) (see [2]), but no one of these satisfies our condition. As a consequence, we obtain the non-existence of Hopf real hypersurfaces in such ambient spaces whose Jacobi operators corresponding to -directions are parallel with the same further condition.展开更多
In this paper, we consider a new notion of generalized Tanaka Webster З-parallel shape operator for a real hypersurface in a complex two-plane Grassrnannian and prove a non-existence theorem of a real hypersurface.
基金Supported by National Research Foundation of Korea(Grant No.NRF-2011-220-1-C00002)partially supported by MCT(Grant No.MTM2010-18099)supported by NRF(Grant No.NRF-2012-R1A2A2A-01043023)
文摘We classify real hypersurfaces in complex two-plane Grassmannians whose structure Jacobi operator commutes either with any other Jacobi operator or with the normal Jacobi operator.
文摘We prove the non-existence of Hopf real hypersurfaces in complex two-plane Grassmannians whose Jacobi operators or the Jacobi corresponding to the directions in the distribution are of Codazzi type if they satisfy a further condition. We obtain that that they must be either of type (A) or of type (B) (see [2]), but no one of these satisfies our condition. As a consequence, we obtain the non-existence of Hopf real hypersurfaces in such ambient spaces whose Jacobi operators corresponding to -directions are parallel with the same further condition.
基金supported by National Research Foundation of Korea(NRF)(Grant Nos.2012-R1A1A3002031 and 2015-R1A2A1A-01002459)supported by KNU 2015(Bokhyun)Research Fund
文摘In this paper, we consider a new notion of generalized Tanaka Webster З-parallel shape operator for a real hypersurface in a complex two-plane Grassrnannian and prove a non-existence theorem of a real hypersurface.
