Real Hypersurfaces with Quadratic Killing Normal Jacobi Operator in the Real Grassmannians of Rank Two

2021 ◽  
Vol 76 (3) ◽  
Author(s):  
Hyunjin Lee ◽  
Young Jin Suh
Keyword(s):  
Jacobi Operator ◽  
Real Hypersurfaces ◽  
The Real ◽  
Normal Jacobi Operator

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.

The normal Jacobi operator of real hypersurfaces in complex hyperbolic two-plane Grassmannians

2015 ◽  
Vol 26 (09) ◽  
pp. 1550075
Author(s):  
Konstantina Panagiotidou ◽  
Juan De Dios Pérez
Keyword(s):  
Jacobi Operator ◽  
Real Hypersurfaces ◽  
Normal Jacobi Operator

The aim of this paper is to introduce the notion of normal Jacobi operator of real hypersurfaces in complex hyperbolic two-plane Grassmannians. Furthermore, results concerning real hypersurfaces in complex hyperbolic two-plane Grassmannians whose normal Jacobi operator satisfies conditions of parallelism will be given.

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