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Real Hypersurfaces in the Complex Hyperbolic Quadric with Killing Shape Operator

서영진|정임순
경북대학교 자연과학대학 수학과|2017.12|Kyungpook Mathematical Journal|제57권 제4호|pp. 683-699

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참고문헌

키워드

complex conjugationKilling shape operator$\mathfrak A$-isotropic$\mathfrak A$-principalK\"{a}hler structurecomplex quadric.
주제분류수학

초록

We introduce the notion of Killing shape operator for real hypersurfaces in the complex hyperbolic quadric ${Q^m}^* = SO_{m,2}/SO_mSO_2$. The Killing shape operator implies that the unit normal vector field $N$ becomes$\mathfrak A$-principal or $\mathfrak A$-isotropic. Then according to each case, we give a complete classification of real hypersurfaces in ${Q^m}^* = SO_{m,2}/SO_mSO_2$ with Killing shape operator.

Abstract

We introduce the notion of Killing shape operator for real hypersurfaces in the complex hyperbolic quadric ${Q^m}^* = SO_{m,2}/SO_mSO_2$. The Killing shape operator implies that the unit normal vector field $N$ becomes$\mathfrak A$-principal or $\mathfrak A$-isotropic. Then according to each case, we give a complete classification of real hypersurfaces in ${Q^m}^* = SO_{m,2}/SO_mSO_2$ with Killing shape operator.

참고문헌 (24)

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