scholarly journals Marginally trapped submanifolds in Lorentzian space forms and in the Lorentzian product of a space form by the real line

2015 ◽  
Vol 56 (2) ◽  
pp. 023502 ◽  
Author(s):  
Henri Anciaux ◽  
Yamile Godoy
Keyword(s):  
Real Line ◽  
Space Form ◽  
Space Forms ◽  
Lorentzian Space ◽  
The Real ◽  
Lorentzian Space Forms

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.

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

scholarly journals Quasi-Einstein Hypersurfaces of Complex Space Forms

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Xiaomin Chen ◽  
Xuehui Cui
Keyword(s):  
Real Hypersurface ◽  
Complex Space ◽  
Space Form ◽  
Ricci Soliton ◽  
Complex Space Form ◽  
Einstein Metric ◽  
Space Forms ◽  
The Real ◽  
Complex Euclidean Space ◽  
Complex Space Forms

Based on a well-known fact that there are no Einstein hypersurfaces in a nonflat complex space form, in this article, we study the quasi-Einstein condition, which is a generalization of an Einstein metric, on the real hypersurface of a nonflat complex space form. For the real hypersurface with quasi-Einstein metric of a complex Euclidean space, we also give a classification. Since a gradient Ricci soliton is a special quasi-Einstein metric, our results improve some conclusions of Cho and Kimura.

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.

Conformal CMC-Surfaces in Lorentzian Space Forms*

2007 ◽  
Vol 28 (3) ◽  
pp. 299-310 ◽  
Author(s):  
Changxiong Nie ◽  
Xiang Ma ◽  
Changping Wang
Keyword(s):  
Space Forms ◽  
Lorentzian Space ◽  
Cmc Surfaces ◽  
Lorentzian Space Forms
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