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References (41)
-
M. Gaffney (1954)
A Special Stokes's Theorem for Complete Riemannian ManifoldsAnnals of Mathematics, 60
-
Biaogui Yang (2010)
ON COMPLETE SPACELIKE (r-1)-MAXIMAL HYPERSURFACES IN THE ANTI-DE SITTER SPACE H 1 n+1Bulletin of The Korean Mathematical Society, 47
-
N Abe (1987)
123Yokohama Math. J., 35
-
C. Aquino, H. Baltazar, H. Lima (2020)
New characterizations of spacelike hyperplanes in the steady state spaceMathematica Scandinavica, 126
-
C. Aquino, H. Baltazar, H. Lima (2019)
Characterizing horospheres of the hyperbolic space via higher order mean curvaturesDifferential Geometry and its Applications
-
C. Aquino, H. Lima (2014)
On the umbilicity of complete constant mean curvature spacelike hypersurfacesMathematische Annalen, 360
-
D. Ferus (1971)
On the completeness of nullity foliations.Michigan Mathematical Journal, 18
-
B. Wu (2010)
ON COMPLETE SPACELIKE HYPERSURFACES WITH CONSTANT m -TH MEAN CURVATURE IN AN ANTI-DE SITTER SPACEInternational Journal of Mathematics, 21
-
A. Caminha (2009)
The geometry of closed conformal vector fields on Riemannian spacesBulletin of the Brazilian Mathematical Society, New Series, 42
-
J. Senovilla (2006)
Singularity Theorems in General Relativity: Achievements and Open Questions, 12
-
K. Tenenblat (1971)
On isometric immersions of riemannian manifoldsBoletim da Sociedade Brasileira de Matemática, 2
-
C. Aquino, H. Lima, M. Velásquez (2015)
On the geometry of complete spacelike hypersurfaces in the anti-de Sitter spaceGeometriae Dedicata, 174
-
S. Weinberg, R. Wagoner (1973)
Gravitation and Cosmology: Principles and Applications of the General Theory of RelativityPhysics Today, 26
-
R Wald (1984)
10.7208/chicago/9780226870373.001.0001General relativity
-
Linfen Cao, G. Wei (2007)
A new characterization of hyperbolic cylinder in anti-de Sitter space H1n+1(−1)Journal of Mathematical Analysis and Applications, 329
-
G. Galloway, J. Senovilla (2010)
Singularity theorems based on trapped submanifolds of arbitrary co-dimensionClassical and Quantum Gravity, 27
-
H. Rosenberg (1993)
Hypersurfaces of constant curvature in space formsBulletin Des Sciences Mathematiques, 117
-
D. Raine (2021)
General relativityNature, 283
-
(1965)
Gravitational collapse and space-time singularities -
A. Caminha (2006)
A rigidity theorem for complete CMC hypersurfaces in Lorentz manifoldsDifferential Geometry and Its Applications, 24
-
(1983)
Semi-riemannian geometrywith applications to relativity -
H Omori (1967)
Isometric immersions of Riemannian manifoldsJ. Math. Soc. Japan, 19
-
J. Grant (2009)
GLOBAL LORENTZIAN GEOMETRY -
P Lucas, HF Ramírez-Ospina (2012)
Hypersurfaces in non-flat Lorentzian space forms satisfying Lkψ=Aψ+b\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_k\psi =A\psi +b$$\end{document}Taiwanese J. Math., 16
-
(1976)
Some function-theoretic properties of complete Riemannianmanifolds and their applications to geometry -
F. Camargo, H. Lima (2010)
New characterizations of totally geodesic hypersurfaces in anti-de Sitter space H1n+1Journal of Geometry and Physics, 60
-
L. Alías, A. Brasil, A. Colares (2003)
INTEGRAL FORMULAE FOR SPACELIKE HYPERSURFACES IN CONFORMALLY STATIONARY SPACETIMES AND APPLICATIONSProceedings of the Edinburgh Mathematical Society, 46
-
S. Yau (1975)
Harmonic functions on complete riemannian manifoldsCommunications on Pure and Applied Mathematics, 28
-
P. Lucas, H. Ramirez-Ospina (2012)
HYPERSURFACES IN NON-FLAT LORENTZIAN SPACE FORMS SATISFYING Lkψ = Aψ + bTaiwanese Journal of Mathematics, 16
-
L. Alías, A. Colares (2007)
Uniqueness of spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson–Walker spacetimesMathematical Proceedings of the Cambridge Philosophical Society, 143
-
H. Lima, M. Velásquez (2013)
On the geometry of linear Weingarten spacelike hypersurfaces in the de Sitter spaceBulletin of the Brazilian Mathematical Society, New Series, 44
-
M. Modgil (2010)
Interplay between the small and the large scale structure of spacetimearXiv: General Physics
-
M. Dajczer (1990)
Submanifolds and isometric immersions -
SW Hawking, GFR Ellis (1973)
10.1017/CBO9780511524646The large scale structure of spacetime
-
R. Chaves, L. Sousa, B. Valério (2012)
New characterizations for hyperbolic cylinders in anti-de Sitter spacesJournal of Mathematical Analysis and Applications, 393
-
O. Perdomo (2009)
New examples of maximal space like surfaces in the anti-de Sitter spaceJournal of Mathematical Analysis and Applications, 353
-
S. Montiel (1999)
Uniqueness of spacelike hypersurfaces of constant mean curvature in foliated spacetimesMathematische Annalen, 314
-
SM Choi, U-H Ki, H-J Kim (1994)
Complete maximal spacelike hypersurfaces in an anti-de Sitter spaceBull. Korean Math. Soc., 31
-
N. Abe, N. Koike, S. Yamaguchi (1987)
CONGRUENCE THEOREMS FOR PROPER SEMI- RIEMANNIAN HYPERSURFACES IN A REAL SPACE FORM, 35
-
Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations -
F. Camargo, A. Caminha, H. Lima, Ulisses Parente (2012)
Generalized maximum principles and the rigidity of complete spacelike hypersurfacesMathematical Proceedings of the Cambridge Philosophical Society, 153
- Publisher
- Springer Journals
- Copyright
- Copyright © The Author(s) under exclusive license to Università degli Studi di Ferrara 2022
- ISSN
- 0430-3202
- eISSN
- 1827-1510
- DOI
- 10.1007/s11565-022-00403-y
- Publisher site
- See Article on Publisher Site
Abstract
Our aim in this paper is to study the uniqueness of complete spacelike hypersurfaces immersed in the anti-de Sitter space H1n+1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{\mathbb {H}}}_1^{n+1}$$\end{document}, through the behavior of their higher order mean curvatures. This is done by applying a suitable maximum principle concerning smooth vector fields whose norm is Lebesgue integrable on a complete Riemannian manifold. We also infer the nullity of complete r-maximal spacelike hypersurfaces and, in particular, we establish a nonexistence result concerning complete 1-maximal spacelike hypersurfaces in H1n+1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{\mathbb {H}}}_1^{n+1}$$\end{document}.
Journal
ANNALI DELL UNIVERSITA DI FERRARA – Springer Journals
Published: May 1, 2023
Keywords: Anti-de Sitter space; Complete spacelike hypersurfaces; Totally umbilical spacelike hypersurfaces; Higher order mean curvatures; r-maximal hypersurfaces; Index of nullity; Primary 53C42; Secondary 53B30; 53C50