# Hopf Hypersurfaces in Complex Two-plane Grassmannians with Generalized Tanaka-Webster Reeb-parallel Structure Jacobi Operator

• Kim, Byung Hak (Department of Applied Mathematics and Institute of Natural Sciences, Kyung Hee University) ;
• Lee, Hyunjin (The Research Institute of Real and Complex Manifolds, Kyungpook National University) ;
• Pak, Eunmi (Department of Mathematics, Kyungpook National University)
• Accepted : 2018.02.27
• Published : 2019.09.23
• 15 2

#### Abstract

In relation to the generalized Tanaka-Webster connection, we consider a new notion of parallel structure Jacobi operator for real hypersurfaces in complex two-plane Grassmannians and prove the non-existence of real hypersurfaces in $G_2({\mathbb{C}}^{m+2})$ with generalized Tanaka-Webster parallel structure Jacobi operator.

#### Keywords

real hypersurface;complex two-plane Grassmannian;Hopf hypersurface;generalized Tanaka-Webster connection;structure Jacobi operator

#### Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

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