scholarly journals ANTI-COMMUTING REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS

2008 ◽  
Vol 78 (2) ◽  
pp. 199-210 ◽  
Author(s):  
IMSOON JEONG ◽  
HYUN JIN LEE ◽  
YOUNG JIN SUH
Keyword(s):  
Shape Operator ◽  
Real Hypersurfaces ◽  
Nonexistence Theorem ◽  
Commuting Shape Operator

AbstractIn this paper we give a nonexistence theorem for real hypersurfaces in complex two-plane Grassmannians G2(ℂm+2) with anti-commuting shape operator.

scholarly journals Real Hypersurfaces in complex hyperbolic two-plane Grassmannians with commuting shape operator

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Juan de Dios Pérez ◽  
Young Jin Suh ◽  
Changhwa Woo
Keyword(s):  
Shape Operator ◽  
Real Hypersurfaces ◽  
Commuting Shape Operator

AbstractIn this paper we prove a non-existence of real hypersurfaces in complex hyperbolic two-plane Grassmannians SU

scholarly journals Real hypersurfaces in complex two-plane Grassmannians with commuting shape operator

2003 ◽  
Vol 68 (3) ◽  
pp. 379-393 ◽  
Author(s):  
Young Jin Suh
Keyword(s):  
Shape Operator ◽  
Real Hypersurfaces ◽  
View Point ◽  
Existence Property ◽  
Commuting Shape Operator ◽  
Structure Tensors

In this paper we give a non-existence property of real hypersurfaces in complex two-plane Grassmannians G2(ℂm+2) which have a shape operator A commuting with the structure tensors {φ1, φ2, φ3}. From this view point we give a characterisation of real hypersurfaces of type B in G2(ℂm+2).

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.

Remarks on η-parallel real hypersurfaces in ℂP2 and ℂH2

2020 ◽  
Vol 17 (05) ◽  
pp. 2050073
Author(s):  
Yaning Wang
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Three Dimensional ◽  
Shape Operator ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
Geodesic Sphere ◽  
Principal Curvatures ◽  
Space Forms ◽  
Complex Dimension

Let [Formula: see text] be a three-dimensional real hypersurface in a nonflat complex space form of complex dimension two. In this paper, we prove that [Formula: see text] is [Formula: see text]-parallel with two distinct principal curvatures at each point if and only if it is locally congruent to a geodesic sphere in [Formula: see text] or a horosphere, a geodesic sphere or a tube over totally geodesic complex hyperbolic plane in [Formula: see text]. Moreover, [Formula: see text]-parallel real hypersurfaces in [Formula: see text] and [Formula: see text] under some other conditions are classified and these results extend Suh’s in [Characterizations of real hypersurfaces in complex space forms in terms of Weingarten map, Nihonkai Math. J. 6 (1995) 63–79] and Kon–Loo’s in [On characterizations of real hypersurfaces in a complex space form with [Formula: see text]-parallel shape operator, Canad. Math. Bull. 55 (2012) 114–126].

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

Real Hypersurfaces in Complex Two-Plane Grassmannians with Vanishing Lie Derivative

2006 ◽  
Vol 49 (1) ◽  
pp. 134-143 ◽  
Author(s):  
Young Jin Suh
Keyword(s):  
Vector Field ◽  
Shape Operator ◽  
Real Hypersurfaces ◽  
Lie Derivative ◽  
Reeb Vector ◽  
Totally Geodesic ◽  
Reeb Vector Field

AbstractIn this paper we give a characterization of real hypersurfaces of type A in a complex two-plane Grassmannian G2(ℂm+2) which are tubes over totally geodesic G2(ℂm+1) in G2(ℂm+2) in terms of the vanishing Lie derivative of the shape operator A along the direction of the Reeb vector field ξ.

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