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arXiv 2003.072312020-03-13math.DG

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

Hyunjin Lee, Young Jin Suh

备注：: 20 pages. arXiv admin note: text overlap with arXiv:1907.04661, arXiv:1605.05316
DOI：: 10.1007/s11040-020-09370-2

英文摘要：

In this paper, first, we investigate the commuting property between the normal Jacobi operator~${\bar R}_N$ and the structure Jacobi operator~$R_ξ$ for Hopf real hypersurfaces in the complex quadric~$Q^m = SO_{m+2}/SO_mSO_2$, $m \geq 3$, which is defined by ${\bar R}_N R_ξ = R_ξ{\bar R}_N$. 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.

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