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.

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.

scholarly journals Commuting Conditions of the k-th Cho operator with the structure Jacobi operator of real hypersurfaces in complex space forms

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Konstantina Panagiotidou ◽  
Juan de Dios Pérez
Keyword(s):  
Vector Field ◽  
Hyperbolic Space ◽  
Complex Space ◽  
Jacobi Operator ◽  
Three Dimensional ◽  
Complex Hyperbolic Space ◽  
Real Hypersurfaces ◽  
Space Forms ◽  
Structure Jacobi Operator ◽  
Complex Space Forms

AbstractIn this paper three dimensional real hypersurfaces in non-flat complex space forms whose k-th Cho operator with respect to the structure vector field ξ commutes with the structure Jacobi operator are classified. Furthermore, it is proved that the only three dimensional real hypersurfaces in non-flat complex space forms, whose k-th Cho operator with respect to any vector field X orthogonal to structure vector field commutes with the structure Jacobi operator, are the ruled ones. Finally, results concerning real hypersurfaces in complex hyperbolic space satisfying the above conditions are also provided.

scholarly journals Ruled real hypersurfaces of complex space forms

2010 ◽  
Vol 33 (1) ◽  
pp. 123-134 ◽  
Author(s):  
Tatsuyoshi Hamada ◽  
Jun-ichi Inoguchi
Keyword(s):  
Complex Space ◽  
Real Hypersurfaces ◽  
Space Forms ◽  
Ruled Real Hypersurfaces ◽  
Complex Space Forms

scholarly journals A Characterization of Ruled Real Hypersurfaces in Non-Flat Complex Space Forms

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 642
Author(s):  
George Kaimakamis ◽  
Konstantina Panagiotidou ◽  
Juan de Dios Pérez
Keyword(s):  
Ricci Tensor ◽  
Complex Space ◽  
Space Form ◽  
Flat Space ◽  
Real Hypersurfaces ◽  
Space Forms ◽  
Ruled Real Hypersurfaces ◽  
Levi Civita Connection ◽  
Complex Space Forms

The Levi-Civita connection and the k-th generalized Tanaka-Webster connection are defined on a real hypersurface M in a non-flat complex space form. For any nonnull constant k and any vector field X tangent to M the k-th Cho operator F X ( k ) is defined and is related to both connections. If X belongs to the maximal holomorphic distribution D on M, the corresponding operator does not depend on k and is denoted by F X and called Cho operator. In this paper, real hypersurfaces in non-flat space forms such that F X S = S F X , where S denotes the Ricci tensor of M and a further condition is satisfied, are classified.

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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