scholarly journals Real hypersurfaces in the complex quadric with Reeb invariant shape operator

2015 ◽  
Vol 38 ◽  
pp. 10-21 ◽  
Author(s):  
Young Jin Suh
Keyword(s):  
Shape Operator ◽  
Real Hypersurfaces ◽  
Complex Quadric ◽  
Invariant Shape

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.

Real Hypersurfaces with Killing Shape Operator in the Complex Quadric

2017 ◽  
Vol 15 (1) ◽  
Author(s):  
Juan de Dios Pérez ◽  
Imsoon Jeong ◽  
Junhyung Ko ◽  
Young Jin Suh
Keyword(s):  
Shape Operator ◽  
Real Hypersurfaces ◽  
Complex Quadric

scholarly journals REAL HYPERSURFACES WITH φ-INVARIANT SHAPE OPERATOR IN A COMPLEX PROJECTIVE SPACE

2010 ◽  
Vol 53 (2) ◽  
pp. 347-358 ◽  
Author(s):  
SADAHIRO MAEDA ◽  
HIROO NAITOH
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Shape Operator ◽  
Type A ◽  
Real Hypersurfaces ◽  
Ruled Real Hypersurfaces ◽  
Shape Operators ◽  
Complex Projective ◽  
Invariant Shape

AbstractWe characterize real hypersurfaces of type (A) and ruled real hypersurfaces in a complex projective space in terms of two φ-invariances of their shape operators, and give geometric meanings of these real hypersurfaces by observing their some geodesics.

Real hypersurfaces in the complex quadric with generalized Killing shape operator

2021 ◽  
Vol 159 ◽  
pp. 103800 ◽  
Author(s):  
Hyunjin Lee ◽  
Doo Hyun Hwang ◽  
Young Jin Suh
Keyword(s):  
Shape Operator ◽  
Real Hypersurfaces ◽  
Complex Quadric

Some new results on real hypersurfaces with generalized Tanaka-Webster connection

2019 ◽  
Vol 69 (3) ◽  
pp. 665-674
Author(s):  
Wenjie Wang ◽  
Ximin Liu
Keyword(s):  
Real Hypersurface ◽  
Complex Space ◽  
Shape Operator ◽  
Real Hypersurfaces ◽  
Space Forms ◽  
Complex Dimension ◽  
Nonflat Complex Space Forms ◽  
Complex Space Forms ◽  
Ruled Real Hypersurface

Abstract Let M be a real hypersurface in nonflat complex space forms of complex dimension two. In this paper, we prove that the shape operator of M is transversally Killing with respect to the generalized Tanaka-Webster connection if and only if M is locally congruent to a type (A) or (B) real hypersurface. We also prove that shape operator of M commutes with Cho operator on holomorphic distribution if and only if M is locally congruent to a ruled real hypersurface.

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