Cyclic η-parallel shape and Ricci operators on real hypersurfaces in two-dimensional nonflat complex space forms

2019 ◽  
Vol 302 (1) ◽  
pp. 335-352 ◽  
Author(s):  
Yaning Wang
Keyword(s):  
Complex Space ◽  
Real Hypersurfaces ◽  
Two Dimensional ◽  
Space Forms ◽  
Nonflat Complex Space Forms ◽  
Complex Space Forms

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.

Derivatives on Real Hypersurfaces of Two-Dimensional Non-flat Complex Space Forms

2017 ◽  
Vol 14 (2) ◽  
Author(s):  
George Kaimakamis ◽  
Konstantina Panagiotidou ◽  
Juan de Dios Pérez
Keyword(s):  
Complex Space ◽  
Real Hypersurfaces ◽  
Two Dimensional ◽  
Space Forms ◽  
Complex Space Forms

scholarly journals Existence and uniqueness of inhomogeneous ruled hypersurfaces with shape operator of constant norm in the complex hyperbolic space

2021 ◽  
pp. 2150049
Author(s):  
Miguel Domínguez-Vázquez ◽  
Olga Pérez-Barral
Keyword(s):  
Hyperbolic Space ◽  
Complex Space ◽  
Shape Operator ◽  
Complex Hyperbolic Space ◽  
Real Hypersurfaces ◽  
Space Forms ◽  
Nonflat Complex Space Forms ◽  
Ruled Real Hypersurfaces ◽  
Complex Space Forms

We complete the classification of ruled real hypersurfaces with shape operator of constant norm in nonflat complex space forms by showing the existence of a unique inhomogeneous example in the complex hyperbolic space.

REAL HYPERSURFACES IN COMPLEX SPACE FORMS ATTAINING EQUALITY IN AN INEQUALITY INVOLVING A CONTACT δ-INVARIANT

2020 ◽  
pp. 1-8
Author(s):  
TORU SASAHARA
Keyword(s):  
Complex Space ◽  
Real Hypersurfaces ◽  
Space Forms ◽  
Nonflat Complex Space Forms ◽  
Complex Space Forms

Abstract We investigate real hypersurfaces in nonflat complex space forms attaining equality in an inequality involving the contact δ-invariant δ c (2) introduced by Chen and Mihai in [3].

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