scholarly journals Real Hypersurfaces in the Complex Hyperbolic Quadric with Reeb Parallel Structure Jacobi Operator

2020 ◽  
Vol 23 (1) ◽  
Author(s):  
Hyunjin Lee ◽  
Young Jin Suh
Keyword(s):  
Jacobi Operator ◽  
Parallel Structure ◽  
Real Hypersurfaces ◽  
Structure Jacobi Operator ◽  
Hyperbolic Quadric ◽  
Complex Hyperbolic Quadric

scholarly journals REAL HYPERSURFACES WITH CYCLIC-PARALLEL STRUCTURE JACOBI OPERATORS IN A NONFLAT COMPLEX SPACE FORM

2009 ◽  
Vol 81 (2) ◽  
pp. 260-273 ◽  
Author(s):  
U-HANG KI ◽  
HIROYUKI KURIHARA
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Jacobi Operator ◽  
Complex Space Form ◽  
Parallel Structure ◽  
Real Hypersurfaces ◽  
Structure Jacobi Operator ◽  
Jacobi Operators

AbstractIt is known that there are no real hypersurfaces with parallel structure Jacobi operators in a nonflat complex space form. In this paper, we classify real hypersurfaces in a nonflat complex space form whose structure Jacobi operator is cyclic-parallel.

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.

Real Hypersurfaces in Complex Two-Plane Grassmannians with Reeb Parallel Structure Jacobi Operator

2014 ◽  
Vol 57 (4) ◽  
pp. 821-833 ◽  
Author(s):  
Imsoon Jeong ◽  
Seonhui Kim ◽  
Young Jin Suh
Keyword(s):  
Real Hypersurface ◽  
Jacobi Operator ◽  
Parallel Structure ◽  
Real Hypersurfaces ◽  
Structure Jacobi Operator ◽  
Totally Geodesic

AbstractIn this paper we give a characterization of a real hypersurface of Type (A) in complex two-plane GrassmanniansG2(ℂm+2), which means a tube over a totally geodesicG2(ℂm+1) inG2(ℂm+2), by means of the Reeb parallel structure Jacobi operator ∇εRε= 0.

REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS WITH 𝔇⊥-PARALLEL STRUCTURE JACOBI OPERATOR

2011 ◽  
Vol 22 (05) ◽  
pp. 655-673 ◽  
Author(s):  
IMSOON JEONG ◽  
CARLOS J. G. MACHADO ◽  
JUAN DE DIOS PÉREZ ◽  
YOUNG JIN SUH
Keyword(s):  
Existence Theorems ◽  
Jacobi Operator ◽  
Parallel Structure ◽  
Real Hypersurfaces ◽  
Structure Jacobi Operator

In this paper we give some non-existence theorems for Hopf real hypersurfaces in complex two-plane Grassmannians G2(ℂm+2) with 𝔇⊥-parallel structure Jacobi operator, where 𝔇⊥= Span {ξ1, ξ2, ξ3}.

Cyclic parallel structure Jacobi operator for real hypersurfaces in complex two-plane Grassmannians

2021 ◽  
pp. 1-26
Author(s):  
Hyunjin Lee ◽  
Young Jin Suh ◽  
Changhwa Woo
Keyword(s):  
Jacobi Operator ◽  
Parallel Structure ◽  
Real Hypersurfaces ◽  
Structure Jacobi Operator ◽  
Equivalent Relation

In this paper, from the property of Killing for structure Jacobi tensor $\mathbb {R}_{\xi }$ , we introduce a new notion of cyclic parallelism of structure Jacobi operator $R_{\xi }$ on real hypersurfaces in the complex two-plane Grassmannians. By virtue of geodesic curves, we can give the equivalent relation between cyclic parallelism of $R_{\xi }$ and Killing property of $\mathbb {R}_{\xi }$ . Then, we classify all Hopf real hypersurfaces with cyclic parallel structure Jacobi operator in complex two-plane Grassmannians.

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