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.

scholarly journals On ruled real hypersurfaces in a complex space form

1993 ◽  
Vol 17 (2) ◽  
pp. 311-322 ◽  
Author(s):  
Seong-Soo Ahn ◽  
Sung-Baik Lee ◽  
Young-Jin Suh
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
Ruled Real Hypersurfaces

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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