scholarly journals CERTAIN RESULTS OF REAL HYPERSURFACES IN A COMPLEX SPACE FORM

2011 ◽  
Vol 54 (1) ◽  
pp. 1-8 ◽  
Author(s):  
AMALENDU GHOSH
Keyword(s):  
Real Hypersurface ◽  
Complex Space ◽  
Space Form ◽  
Ricci Soliton ◽  
Complex Space Form ◽  
Real Hypersurfaces

AbstractFirst, we classify a real hypersurface of a non-flat complex space form with (i) semi-parallel T(=£ξg), and (ii) recurrent T. Next, we characterise a real hypersurface admitting the generalised η-Ricci soliton in a non-flat complex space form.

scholarly journals Quasi-Einstein Hypersurfaces of Complex Space Forms

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Xiaomin Chen ◽  
Xuehui Cui
Keyword(s):  
Real Hypersurface ◽  
Complex Space ◽  
Space Form ◽  
Ricci Soliton ◽  
Complex Space Form ◽  
Einstein Metric ◽  
Space Forms ◽  
The Real ◽  
Complex Euclidean Space ◽  
Complex Space Forms

Based on a well-known fact that there are no Einstein hypersurfaces in a nonflat complex space form, in this article, we study the quasi-Einstein condition, which is a generalization of an Einstein metric, on the real hypersurface of a nonflat complex space form. For the real hypersurface with quasi-Einstein metric of a complex Euclidean space, we also give a classification. Since a gradient Ricci soliton is a special quasi-Einstein metric, our results improve some conclusions of Cho and Kimura.

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 On pseudo-Einstein real hypersurfaces

2020 ◽  
Vol 20 (4) ◽  
pp. 559-571
Author(s):  
Mayuko Kon
Keyword(s):  
Ricci Tensor ◽  
Real Hypersurface ◽  
Vector Fields ◽  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
Definition Of ◽  
Weaker Conditions

AbstractLet M be a real hypersurface of a complex space form Mn(c) with c ≠ 0 and n ≥ 3. We show that the Ricci tensor S of M satisfies S(X, Y) = ag(X, Y) for all vector fields X and Y on the holomorphic distribution, a being a constant, if and only if M is a pseudo-Einstein real hypersurface. By doing this we can give the definition of pseudo-Einstein real hypersurface under weaker conditions.

scholarly journals Generating Curves of Minimal Ruled Real Hypersurfaces in a Nonflat Complex Space Form

2019 ◽  
Vol 62 (02) ◽  
pp. 383-392 ◽  
Author(s):  
Sadahiro Maeda ◽  
Hiromasa Tanabe ◽  
Seiichi Udagawa
Keyword(s):  
Real Hypersurface ◽  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
Ruled Real Hypersurfaces ◽  
Integral Curves ◽  
Necessary And Sufficient ◽  
Characteristic Vector Field ◽  
Ruled Real Hypersurface

AbstractWe first provide a necessary and sufficient condition for a ruled real hypersurface in a nonflat complex space form to have constant mean curvature in terms of integral curves of the characteristic vector field on it. This yields a characterization of minimal ruled real hypersurfaces by circles. We next characterize the homogeneous minimal ruled real hypersurface in a complex hyperbolic space by using the notion of strong congruency of curves.

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.

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].

scholarly journals Ricci operator in a Hopf real Hypersurfaces of complex space form

2020 ◽  
Vol 1597 ◽  
pp. 012049
Author(s):  
Uppara Manjulamma ◽  
H G Nagaraja ◽  
D L Kiran Kumar
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
Ricci Operator
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