scholarly journals A characterization of hyperbolic cylinders in the de Sitter space

1996 ◽  
Vol 48 (1) ◽  
pp. 23-31 ◽  
Author(s):  
Sebastián Montiel
Keyword(s):  
De Sitter Space ◽  
De Sitter ◽  
Hyperbolic Cylinders

scholarly journals Weingarten spacelike hypersurfaces in a de Sitter space

2012 ◽  
Vol 20 (1) ◽  
pp. 387-406
Author(s):  
Junfeng Chen ◽  
Shichang Shu
Keyword(s):  
De Sitter Space ◽  
De Sitter ◽  
Principal Curvatures ◽  
Riemannian Product ◽  
Spacelike Hypersurfaces ◽  
Hyperbolic Cylinder

Abstract We study some Weingarten spacelike hypersurfaces in a de Sitter space S1n+1 (1). If the Weingarten spacelike hypersurfaces have two distinct principal curvatures, we obtain two classification theorems which give some characterization of the Riemannian product Hk(1−coth2 ϱ)× Sn−k(1 − tanh2 ϱ), 1 < k < n − 1 in S1n+1(1), the hyperbolic cylinder H1(1 − coth2 ϱ) × Sn-1(1 − tanh2 ϱ) or spherical cylinder Hn−1(1 − coth2 ϱ) × S1(1 − tanh2 ϱ) in S1n+1 (1)

scholarly journals Compact Spacelike Hypersurfaces with Constant Mean Curvature in the Antide Sitter Space

2009 ◽  
Vol 2009 ◽  
pp. 1-12
Author(s):  
Henrique F. de Lima ◽  
Joseilson R. de Lima
Keyword(s):  
Hyperbolic Space ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Spacelike Hypersurface ◽  
De Sitter Space ◽  
De Sitter ◽  
Height Estimate ◽  
Spacelike Hypersurfaces ◽  
Hyperbolic Domains

We obtain a height estimate concerning to a compact spacelike hypersurfaceΣnimmersed with constant mean curvatureHin the anti-de Sitter spaceℍ1n+1, when its boundary∂Σis contained into an umbilical spacelike hypersurface of this spacetime which is isometric to the hyperbolic spaceℍn. Our estimate depends only on the value ofHand on the geometry of∂Σ.As applications of our estimate, we obtain a characterization of hyperbolic domains ofℍ1n+1and nonexistence results in connection with such types of hypersurfaces.

ON COMPLETE SPACELIKE HYPERSURFACES WITH CONSTANT m-TH MEAN CURVATURE IN AN ANTI-DE SITTER SPACE

2010 ◽  
Vol 21 (05) ◽  
pp. 551-569 ◽  
Author(s):  
B. Y. WU
Keyword(s):  
Mean Curvature ◽  
Constant Scalar Curvature ◽  
De Sitter Space ◽  
Second Fundamental Form ◽  
De Sitter ◽  
Principal Curvatures ◽  
Global Rigidity ◽  
Complete Spacelike Hypersurfaces ◽  
Spacelike Hypersurfaces ◽  
Hyperbolic Cylinders

We investigate complete spacelike hypersurfaces in an Anti-de Sitter space with constant m-th mean curvature and two distinct principal curvatures. By using Otsuki's idea, we obtain some global classification results. For their application, we obtain some characterizations for hyperbolic cylinders. We prove that the only complete spacelike hypersurfaces in Anti-de Sitter (n + 1)-spaces (n ≥ 3) of constant mean curvature or constant scalar curvature with two distinct principal curvatures λ and μ satisfying inf (λ - μ)2 > 0 are the hyperbolic cylinders. It is a little surprising that the corresponding result does not hold for m-th mean curvature when m > 2. We also obtain some global rigidity results for hyperbolic cylinders in terms of square length of the second fundamental form.

scholarly journals On new characterization of inextensible flows of space-like curves in de Sitter space

2016 ◽  
Vol 14 (1) ◽  
pp. 946-954 ◽  
Author(s):  
Mustafa Yeneroğlu
Keyword(s):  
De Sitter Space ◽  
De Sitter ◽  
Practical Applications ◽  
Inextensible Flows

AbstractElastica and inextensible flows of curves play an important role in practical applications. In this paper, we construct a new characterization of inextensible flows by using elastica in space. The inextensible flow is completely determined for any space-like curve in de Sitter space $\mathbb{S}_{1}^{3}$. Finally, we give some characterizations for curvatures of a space-like curve in de Sitter space $\mathbb{S}_{1}^{3}$.

scholarly journals The motion of a relativistic charged particle in a homogenous electromagnetic field in De-Sitter space

2018 ◽  
Vol 64 (2) ◽  
pp. 176 ◽  
Author(s):  
Ridvan Cem Demirkol ◽  
Talat Körpinar
Keyword(s):  
Electromagnetic Field ◽  
Charged Particle ◽  
De Sitter Space ◽  
Geometric Characterization ◽  
Antisymmetric Tensor ◽  
De Sitter ◽  
Relativistic Approach ◽  
Relativistic Charged Particle

We discuss the geometric characterization of the trajectoryof a moving charged particle, for the case of a homogeneous electromagnetic…eld, in De-Sitter space when the motion is governed by the Lorentz equa-tion. We employ totally relativistic approach during the discussion and itis based on a systematic use of the four-dimensional Frenet-Serret formulae,which is adapted to the De-Sitter space to determine the worldline geometryof the electromagnetic …eld acting on the particle in De-Sitter space, and ofthe Faraday antisymmetric tensor properties.

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