Commutativity of Cho and normal Jacobi operators on real hypersurfaces in the complex quadric

2019 ◽  
Vol 94 (3-4) ◽  
pp. 359-367
Author(s):  
Juan de Dios Perez ◽  
Young Jin Suh
Keyword(s):  
Real Hypersurfaces ◽  
Jacobi Operators ◽  
Complex Quadric

Real Hypersurfaces in the Complex Quadric with Lie Invariant Structure Jacobi Operator

2019 ◽  
Vol 63 (1) ◽  
pp. 204-221
Author(s):  
Young Jin Suh ◽  
Gyu Jong Kim
Keyword(s):  
Jacobi Operator ◽  
Complete Classification ◽  
Real Hypersurfaces ◽  
Normal Vector ◽  
Invariant Structure ◽  
Normal Vector Field ◽  
Jacobi Operators ◽  
Complex Quadric ◽  
Unit Normal Vector Field

AbstractWe introduce the notion of Lie invariant structure Jacobi operators for real hypersurfaces in the complex quadric $Q^{m}=SO_{m+2}/SO_{m}SO_{2}$. The existence of invariant structure Jacobi operators implies that the unit normal vector field $N$ becomes $\mathfrak{A}$-principal or $\mathfrak{A}$-isotropic. Then, according to each case, we give a complete classification of real hypersurfaces in $Q^{m}=SO_{m+2}/SO_{m}SO_{2}$ with Lie invariant structure Jacobi operators.

Real hypersurfaces in the complex quadric with Reeb parallel shape operator

2014 ◽  
Vol 25 (06) ◽  
pp. 1450059 ◽  
Author(s):  
Young Jin Suh
Keyword(s):  
Shape Operator ◽  
Complete Classification ◽  
Real Hypersurfaces ◽  
Complete Proof ◽  
Complex Quadric ◽  
Parallel Shape Operator ◽  
Codazzi Type ◽  
Reeb Parallel Shape Operator

First, we introduce the notion of shape operator of Codazzi type for real hypersurfaces in the complex quadric Qm = SOm+2/SOmSO2. Next, we give a complete proof of non-existence of real hypersurfaces in Qm = SOm+2/SOmSO2 with shape operator of Codazzi type. Motivated by this result we have given a complete classification of real hypersurfaces in Qm = SOm+2/SOmSO2 with Reeb parallel shape operator.

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