Commuting Jacobi operators on Real hypersurfaces of Type B in the complex quadric

2020/03/13 by Hyunjin Lee, Young Jin Suh · 1 citation
Mathematics · #math.DG #msc:53C40 #msc:53C55

paper · pdf · doi:10.1007/s11040-020-09370-2

20 pages. arXiv admin note: text overlap with arXiv:1907.04661, arXiv:1605.05316

arxiv created 2020/03/13 · arxiv updated 2020/12/30

Abstract

In this paper, first, we investigate the commuting property between the normal Jacobi operator~ R_N and the structure Jacobi operator~R_ξ for Hopf real hypersurfaces in the complex quadric~Q^m = SO_m+2/SO_mSO₂, m ≥ 3, which is defined by R_N R_ξ = R_ξ R_N. Moreover, a new characterization of Hopf real hypersurfaces with \mathfrak A-principal singular normal vector field in the complex quadric~Q^m is obtained. By virtue of this result, we can give a remarkable classification of Hopf real hypersurfaces in the complex quadric~Q^m with commuting Jacobi operators.

Citations

• Real hypersurfaces in the complex quadric with Reeb parallel structure Jacobi operator
• Real hypersurfaces in the complex quadric with parallel structure Jacobi operator

Cited by

• On Hopf hypersurfaces of the complex quadric with constant principal curvatures