Characterization of real hypersurface with anti-derivatives of structure Lie operator in a complex space form

2016 ◽  
Vol 10 ◽  
pp. 2843-2850
Author(s):  
Dong Ho Lim
Keyword(s):  
Real Hypersurface ◽  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
Derivatives Of

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.

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.

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