Real hypersurfaces of type (A) in complex two-plane Grassmannians related to the commuting shape operator

2013 ◽  
Vol 25 (1) ◽  
Author(s):  
Imsoon Jeong ◽  
Young Jin Suh
Keyword(s):  
Shape Operator ◽  
Type A ◽  
Real Hypersurfaces ◽  
Commuting Shape Operator

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.

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).

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.

On a Characterization of Real Hypersurfaces of Type a in a Complex Space Form

1994 ◽  
Vol 37 (2) ◽  
pp. 238-244 ◽  
Author(s):  
U-Hang Ki ◽  
Young-Jin Suh
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Type A ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
Orthogonal Distribution

AbstractIn this paper, under certain conditions on the orthogonal distribution T0, we give a characterization of real hypersurfaces of type A in a complex space form Mn(c), c ≠ 0.

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].

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