Real Hypersurfaces in the Complex Hyperbolic Quadric with Commuting Ricci Tensor

2018 ◽  
Vol 42 (3) ◽  
pp. 1173-1198
Author(s):  
Young Jin Suh ◽  
Doo Hyun Hwang
Keyword(s):  
Ricci Tensor ◽  
Real Hypersurfaces ◽  
Hyperbolic Quadric ◽  
Complex Hyperbolic Quadric ◽  
Commuting Ricci Tensor

Real hypersurfaces in the complex hyperbolic quadric with normal Jacobi operator of Codazzi type

2021 ◽  
Author(s):  
Imsoon Jeong ◽  
Eunmi Pak ◽  
Young Jin Suh
Keyword(s):  
Jacobi Operator ◽  
Complete Classification ◽  
Real Hypersurfaces ◽  
Normal Vector ◽  
Normal Vector Field ◽  
Hyperbolic Quadric ◽  
Complex Hyperbolic Quadric ◽  
Unit Normal Vector Field ◽  
Codazzi Type ◽  
Normal Jacobi Operator

In this paper, we introduce the notion of normal Jacobi operator of Codazzi type for real hypersurfaces in the complex hyperbolic quadric [Formula: see text]. The normal Jacobi operator of Codazzi type implies that the unit normal vector field [Formula: see text] becomes [Formula: see text]-principal or [Formula: see text]-isotropic. Then according to each case, we give a complete classification of Hopf real hypersurfaces in [Formula: see text] with normal Jacobi operator of Codazzi type. The result of the classification shows that no such hypersurfaces exist.

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