The homogeneous ruled real hypersurface in a complex hyperbolic space

2018 ◽  
Vol 109 (1) ◽  
Author(s):  
Makoto Kimura ◽  
Sadahiro Maeda ◽  
Hiromasa Tanabe
Keyword(s):  
Hyperbolic Space ◽  
Real Hypersurface ◽  
Complex Hyperbolic Space ◽  
Homogeneous Ruled Real Hypersurface ◽  
Ruled Real Hypersurface

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.

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