D-einstein real hypersurfaces of quaternionic space forms

2000 ◽  
Vol 178 (1) ◽  
pp. 33-44 ◽  
Author(s):  
Miguel Ortega ◽  
Juan de Dios Pérez
Keyword(s):  
Real Hypersurfaces ◽  
Space Forms ◽  
Quaternionic Space

Naturally reductive homogeneous real hypersurfaces in quaternionic space forms

2003 ◽  
Vol 74 (1) ◽  
pp. 87-100
Author(s):  
Setsuo Nagai
Keyword(s):  
Projective Space ◽  
Hyperbolic Space ◽  
Real Hypersurfaces ◽  
Quaternionic Projective Space ◽  
Space Forms ◽  
The Family ◽  
Quaternionic Hyperbolic Space ◽  
Quaternionic Space ◽  
Naturally Reductive

AbstractWe determine the naturally reductive homogeneous real hypersurfaces in the family of curvature-adapted real hypersurfaces in quaternionic projective space HPn(n ≥ 3). We conclude that the naturally reductive curvature-adapted real hypersurfaces in HPn are Q-quasiumbilical and vice-versa. Further, we study the same problem in quaternionic hyperbolic space HHn(n ≥ 3).

scholarly journals Curvature-adapted real hypersurfaces in quaternionic space forms

2001 ◽  
Vol 24 (1) ◽  
pp. 98-119 ◽  
Author(s):  
Toshiaki Adachi ◽  
Sadahiro Maeda
Keyword(s):  
Real Hypersurfaces ◽  
Space Forms ◽  
Quaternionic Space

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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