scholarly journals On isoparametric hypersurfaces in the Lorentzian space forms

1981 ◽  
Vol 7 (1) ◽  
pp. 217-226 ◽  
Author(s):  
Katsumi NOMIZU
Keyword(s):  
Space Forms ◽  
Isoparametric Hypersurfaces ◽  
Lorentzian Space ◽  
Lorentzian Space Forms

Classification of the Blaschke Isoparametric Hypersurfaces in Lorentzian Space Forms

2015 ◽  
Vol 65 (3) ◽  
Author(s):  
Fengyun Zhang ◽  
Huafei Sun
Keyword(s):  
Conformal Transformation ◽  
Transformation Group ◽  
Second Fundamental Form ◽  
Conformal Metric ◽  
Space Forms ◽  
Isoparametric Hypersurfaces ◽  
Lorentzian Space ◽  
Blaschke Tensor ◽  
Lorentzian Space Forms

AbstractIn this paper, we study regular immersed hypersurfaces in Lorentzian space forms with a conformal metric, a conformal second fundamental form, the conformal Blaschke tensor and a conformal form, which are invariants under the conformal transformation group. We classify all the immersed hypersurfaces in Lorentzian space forms with two distinct constant Blaschke eigenvalues and vanishing conformal form.

scholarly journals HYPERSURFACES IN NON-FLAT LORENTZIAN SPACE FORMS SATISFYING Lkψ = Aψ + b

2012 ◽  
Vol 16 (3) ◽  
pp. 1173-1203 ◽  
Author(s):  
Pascual Lucas ◽  
H. Fabian Ramirez-Ospina
Keyword(s):  
Space Forms ◽  
Lorentzian Space ◽  
Lorentzian Space Forms

On the quadric CMC spacelike hypersurfaces in Lorentzian space forms

2016 ◽  
pp. 1-10
Author(s):  
Cícero P. Aquino ◽  
Henrique F. de Lima ◽  
Fábio R. dos Santos
Keyword(s):  
Space Forms ◽  
Lorentzian Space ◽  
Spacelike Hypersurfaces ◽  
Lorentzian Space Forms

NULL HELICES IN LORENTZIAN SPACE FORMS

2001 ◽  
Vol 16 (30) ◽  
pp. 4845-4863 ◽  
Author(s):  
ANGEL FERRÁNDEZ ◽  
ANGEL GIMÉNEZ ◽  
PASCUAL LUCAS
Keyword(s):  
Minkowski Space ◽  
Complete Classification ◽  
Space Forms ◽  
Lorentzian Space ◽  
Low Dimensions ◽  
Minkowski Space Time ◽  
Minimum Number ◽  
Null Curves ◽  
Lorentzian Space Forms

In this paper we introduce a reference along a null curve in an n-dimensional Lorentzian space with the minimum number of curvatures. That reference generalizes the reference of Bonnor for null curves in Minkowski space–time and it is called the Cartan frame of the curve. The associated curvature functions are called the Cartan curvatures of the curve. We characterize the null helices (that is, null curves with constant Cartan curvatures) in n-dimensional Lorentzian space forms and we obtain a complete classification of them in low dimensions.

scholarly journals Hypersurface Constrained Elasticae in Lorentzian Space Forms

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Óscar J. Garay ◽  
Álvaro Pámpano ◽  
Changhwa Woo
Keyword(s):  
Space Form ◽  
Energy Functional ◽  
Bending Energy ◽  
Space Forms ◽  
Lorentzian Space ◽  
Totally Geodesic ◽  
Critical Curves ◽  
Different Types ◽  
Lorentzian Space Forms

We study geodesics in hypersurfaces of a Lorentzian space formM1n+1(c), which are critical curves of theM1n+1(c)-bending energy functional, for variations constrained to lie on the hypersurface. We characterize critical geodesics showing that they live fully immersed in a totally geodesicM13(c)and that they must be of three different types. Finally, we consider the classification of surfaces in the Minkowski 3-space foliated by critical geodesics.

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