Real Hypersurfaces in the Complex Hyperbolic Quadric with Killing Shape Operator

Imsoon Jeong<br />Young Jin Suh

doi:10.5666/KMJ.2017.57.4.683

Articles

Kyungpook Mathematical Journal 2017; 57(4): 683-699

Published online December 23, 2017

Real Hypersurfaces in the Complex Hyperbolic Quadric with Killing Shape Operator

Imsoon Jeong¹
Young Jin Suh²

Division of Future Capability Education, Pai Chai University, Daejeon 35345, Republic of Korea¹
Department of Mathematics & Research Institute of Real and Complex Manifolds, Kyungpook National University, Daegu 41566, Republic of Korea²

Received: April 24, 2017; Accepted: June 26, 2017

Abstract

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Abstract

We introduce the notion of Killing shape operator for real hypersurfaces in the complex hyperbolic quadric Q^m* = SO_m,₂/SO_mSO₂. The Killing shape operator implies that the unit normal vector field N becomes -principal or -isotropic. Then according to each case, we give a complete classification of real hypersurfaces in Q^m* = SO_m,₂/SO_mSO₂ with Killing shape operator.

Keywords: Killing shape operator, $mathfrak A$-isotropic, $mathfrak A$-principal, K"{a}hler structure, complex conjugation, complex quadric