LIE DERIVATIVE OF SHAPE OPERATOR ON REAL HYPERSURFACES IN A COMPLEX SPACE FORM

2015 ◽  
Vol 98 (7) ◽  
pp. 883-895 ◽  
Author(s):  
Dong Ho Lim ◽  
Woon Ha Sohn
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Shape Operator ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
Lie Derivative

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].

Characterizations of Real Hypersurfaces in a Complex Space Form

2007 ◽  
Vol 50 (1) ◽  
pp. 97-104 ◽  
Author(s):  
In-Bae Kim ◽  
Ki Hyun Kim ◽  
Woon Ha Sohn
Keyword(s):  
Real Hypersurface ◽  
Complex Space ◽  
Space Form ◽  
Shape Operator ◽  
Structure Tensor ◽  
Complex Space Form ◽  
Real Hypersurfaces

AbstractWe study a real hypersurface M in a complex space form Mn(c), c ≠ 0, whose shape operator and structure tensor commute each other on the holomorphic distribution of M.

scholarly journals A characterization of ruled hypersurfaces in complex space forms in terms of the Lie derivative of shape operator

2021 ◽  
Vol 6 (12) ◽  
pp. 14054-14063
Author(s):  
Wenjie Wang ◽  
Keyword(s):  
Real Hypersurface ◽  
Complex Space ◽  
Space Form ◽  
Shape Operator ◽  
Real Hypersurfaces ◽  
Lie Derivative ◽  
Space Forms ◽  
Complex Dimension ◽  
Complex Space Forms

<abstract><p>In this paper, it is proved that if a non-Hopf real hypersurface in a nonflat complex space form of complex dimension two satisfies Ki and Suh's condition (J. Korean Math. Soc., 32 (1995), 161–170), then it is locally congruent to a ruled hypersurface or a strongly $ 2 $-Hopf hypersurface. This extends Ki and Suh's theorem to real hypersurfaces of dimension greater than or equal to three.</p></abstract>

On Characterizations of Real Hypersurfaces in a Complex Space Form with η-Parallel Shape Operator

2012 ◽  
Vol 55 (1) ◽  
pp. 114-126 ◽  
Author(s):  
S. H. Kon ◽  
Tee-How Loo
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Shape Operator ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
Parallel Shape Operator

AbstractIn this paper we study real hypersurfaces in a non-flat complex space form with η-parallel shape operator. Several partial characterizations of these real hypersurfaces are obtained.

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.

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