scholarly journals Sectional curvatures of ruled real hypersurfaces in a complex hyperbolic space

2017 ◽  
Vol 51 ◽  
pp. 1-8 ◽  
Author(s):  
Sadahiro Maeda ◽  
Hiromasa Tanabe
Keyword(s):  
Hyperbolic Space ◽  
Complex Hyperbolic Space ◽  
Real Hypersurfaces ◽  
Ruled Real Hypersurfaces ◽  
Sectional Curvatures

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 Transversal Jacobi Operators in Almost Contact Manifolds

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 31
Author(s):  
Jong Taek Cho ◽  
Makoto Kimura
Keyword(s):  
Riemannian Manifold ◽  
Hyperbolic Space ◽  
Jacobi Operator ◽  
Real Hypersurfaces ◽  
Contact Manifolds ◽  
Jacobi Operators ◽  
Ruled Real Hypersurfaces ◽  
Contact Distribution ◽  
Contact Riemannian Manifold

Along a transversal geodesic γ whose tangent belongs to the contact distribution D, we define the transversal Jacobi operator Rγ=R(·,γ˙)γ˙ on an almost contact Riemannian manifold M. Then, using the transversal Jacobi operator Rγ, we give a new characterization of the Sasakian sphere. In the second part, we characterize the complete ruled real hypersurfaces in complex hyperbolic space.

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