Integral curves of the characteristic vector field of minimal ruled real hypersurfaces in non-flat complex space forms

2019 ◽  
Vol 48 (3) ◽  
pp. 589-609
Author(s):  
Makoto KIMURA ◽  
Sadahiro MAEDA ◽  
Hiromasa TANABE
Keyword(s):  
Vector Field ◽  
Complex Space ◽  
Characteristic Vector ◽  
Real Hypersurfaces ◽  
Space Forms ◽  
Ruled Real Hypersurfaces ◽  
Integral Curves ◽  
Complex Space Forms ◽  
Characteristic Vector Field

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 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.

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.

A Classification of Three-dimensional Real Hypersurfaces in Non-flat Complex Space Forms in Terms of their Generalized Tanaka–Webster Lie Derivative

2016 ◽  
Vol 59 (4) ◽  
pp. 813-823
Author(s):  
George Kaimakamis ◽  
Konstantina Panagiotidou ◽  
Juan de Dios Perez
Keyword(s):  
Vector Field ◽  
Complex Space ◽  
Space Form ◽  
Three Dimensional ◽  
Real Hypersurfaces ◽  
Lie Derivative ◽  
Space Forms ◽  
Levi Civita Connection ◽  
Complex Space Forms

AbstractOn a real hypersurface M in a non-flat complex space form there exist the Levi–Civita and the k-th generalized Tanaka–Webster connections. The aim of this paper is to study three dimensional real hypersurfaces in non-flat complex space forms, whose Lie derivative of the structure Jacobi operatorwith respect to the Levi–Civita connection coincides with the Lie derivative of it with respect to the k-th generalized Tanaka-Webster connection. The Lie derivatives are considered in direction of the structure vector field and in direction of any vector field orthogonal to the structure vector field.

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 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.

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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