scholarly journals Compact spacelike surfaces in the 3-dimensional de Sitter space with non-degenerate second fundamental form

2003 ◽  
Vol 19 (1) ◽  
pp. 97-111 ◽  
Author(s):  
Juan A. Aledo ◽  
Alfonso Romero
Keyword(s):  
Fundamental Form ◽  
De Sitter Space ◽  
Second Fundamental Form ◽  
De Sitter ◽  
3 Dimensional ◽  
Spacelike Surfaces

scholarly journals Complete maximal spacelike surfaces in an anti-de Sitter space {\bf H}^{4}_{2}(c)

2000 ◽  
Vol 42 (1) ◽  
pp. 139-156
Author(s):  
Qing-Ming Cheng
Keyword(s):  
Scalar Curvature ◽  
Constant Scalar Curvature ◽  
De Sitter Space ◽  
Second Fundamental Form ◽  
Spacelike Surface ◽  
De Sitter ◽  
Totally Geodesic ◽  
The Second Fundamental Form ◽  
Spacelike Surfaces ◽  
Hyperbolic Cylinder

In this paper, we prove that if M^2 is a complete maximal spacelike surface of an anti-de Sitter space {\bf H}^{4}_{2}(c) with constant scalar curvature, then S=0, S={-10c\over 11}, S={-4c\over 3} or S=-2c, where S is the squared norm of the second fundamental form of M^{2}. Also(1) S=0 if and only if M^2 is the totally geodesic surface {\bf H}^2(c);(2) S={-4c\over 3} if and only if M^2 is the hyperbolic Veronese surface;(3) S=-2c if and only if M^2 is the hyperbolic cylinder of the totally geodesicsurface {\bf H}^{3}_{1}(c) of {\bf H}^{4}_{2}(c).1991 Mathematics Subject Classifaction 53C40, 53C42.

Complete 3-dimensional λ-translators in the Euclidean space ℝ4

2021 ◽  
pp. 1-54
Author(s):  
Zhi Li ◽  
Guoxin Wei ◽  
Gangyi Chen
Keyword(s):  
Euclidean Space ◽  
Fundamental Form ◽  
Second Fundamental Form ◽  
3 Dimensional ◽  
The Second Fundamental Form

In this paper, we obtain the classification theorems for 3-dimensional complete [Formula: see text]-translators [Formula: see text] with constant squared norm [Formula: see text] of the second fundamental form and constant [Formula: see text] in the Euclidean space [Formula: see text].

scholarly journals Space-like submanifolds with parallel mean curvature in de Sitter spaces

2000 ◽  
Vol 69 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Chongzhen Ouyang ◽  
Zhenqi Li
Keyword(s):  
Fundamental Form ◽  
Mean Curvature ◽  
Curvature Vector ◽  
Second Fundamental Form ◽  
Mean Curvature Vector ◽  
De Sitter ◽  
Parallel Mean Curvature Vector ◽  
Complete Space ◽  
The Second Fundamental Form ◽  
Parallel Mean Curvature

AbstractThis paper investigates complete space-like submainfold with parallel mean curvature vector in the de Sitter space. Some pinching theorems on square of the norm of the second fundamental form are given

Complete linear Weingarten spacelike submanifolds with higher codimension in the de Sitter space

2019 ◽  
Vol 16 (04) ◽  
pp. 1950050 ◽  
Author(s):  
Jogli Gidel da Silva Araújo ◽  
Henrique Fernandes de Lima ◽  
Fábio Reis dos Santos ◽  
Marco Antonio Lázaro Velásquez
Keyword(s):  
Mean Curvature ◽  
Curvature Vector ◽  
De Sitter Space ◽  
Second Fundamental Form ◽  
Index Formula ◽  
Curvature Function ◽  
De Sitter ◽  
Spacelike Submanifold ◽  
Spacelike Submanifolds ◽  
Complete Riemannian Manifolds

We study complete linear Weingarten spacelike submanifolds with arbitrary high codimension [Formula: see text] in the de Sitter space [Formula: see text] of index [Formula: see text] and whose normalized mean curvature vector is parallel. Under suitable restrictions on the values of the mean curvature function and on the norm of the traceless part of the second fundamental form, we prove that such a spacelike submanifold must be either totally umbilical or isometric to a certain hyperbolic cylinder of [Formula: see text]. Our approach is based on the use of a Simons type formula related to an appropriate Cheng–Yau modified operator jointly with an extension of Hopf’s maximum principle for complete Riemannian manifolds.

scholarly journals FINITE PARTICLE CREATION IN 3+1 DE SITTER SPACE

1995 ◽  
Vol 10 (33) ◽  
pp. 2519-2530
Author(s):  
D.J. LAMB ◽  
A.Z. CAPRI ◽  
M. KOBAYASHI
Keyword(s):  
Particle Creation ◽  
De Sitter Space ◽  
Bogoliubov Transformation ◽  
De Sitter ◽  
Stationary Observer ◽  
Definition Of ◽  
Spacelike Surfaces ◽  
Finite Particle

In this paper we calculate the particle creation as seen by a stationary observer in 3+1 de Sitter space. This particle creation is calculated using an observer-dependent geometrically based definition of time which is used to quantize a field on two different spacelike surfaces. The Bogoliubov transformation relating these two quantizations is then calculated and the resulting particle creation is shown to be finite.

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.

Weingarten rotation surfaces in 3-dimensional de Sitter space

2004 ◽  
Vol 79 (1-2) ◽  
pp. 156-168 ◽  
Author(s):  
Huili Liu ◽  
Guili Liu
Keyword(s):  
De Sitter Space ◽  
De Sitter ◽  
3 Dimensional
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