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SEMI-SYMMETRIC STRUCTURE JACOBI OPERATOR FOR REAL HYPERSURFACES IN THE COMPLEX QUADRIC

김규종|정임순|우창화
대한수학회 (The Korean Mathematical Society)|2023.07|대한수학회보 (Bulletin of the KMS)|제60권 제4호|pp. 849-861|DOI 10.4134/BKMS.b220152

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키워드

Hopf hypersurfaceSemi-symmetric structure Jacobi operatorcomplex quadricA-isotropic or A-principal vector fields
주제분류수학

초록

In this paper, we introduce the notion of {\it semi-symmetric structure Jacobi operator } for Hopf real hypersufaces in the complex quad\-ric $Q^m = SO_{m+2}/SO_mSO_2$. Next we prove that there does not exist any Hopf real hypersurface in the complex quadric $Q^m = SO_{m+2}/SO_mSO_2$ with semi-symmetric structure Jacobi operator. As a corollary, we also get a non-existence property of Hopf real hypersurfaces in the complex quadric $Q^m$ with either symmetric (parallel), or recurrent structure Jacobi operator.

Abstract

In this paper, we introduce the notion of {\it semi-symmetric structure Jacobi operator } for Hopf real hypersufaces in the complex quad\-ric $Q^m = SO_{m+2}/SO_mSO_2$. Next we prove that there does not exist any Hopf real hypersurface in the complex quadric $Q^m = SO_{m+2}/SO_mSO_2$ with semi-symmetric structure Jacobi operator. As a corollary, we also get a non-existence property of Hopf real hypersurfaces in the complex quadric $Q^m$ with either symmetric (parallel), or recurrent structure Jacobi operator.

참고문헌 (27)

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