Cohomogeneity One Dynamics on Three Dimensional Minkowski Space
DOI:
https://doi.org/10.15407/mag15.02.155Анотація
У роботі надається класифікація замкнутих і зв'язних груп Лі, з точністю до спряженості в $\mathrm{Iso}({\mathbb{R}^{1,2}})$, що діє з кооднорідністю один на тривимірному просторі Мінковського $\mathbb{R}^{1,2}$ як для власної, так і невласної динаміки. Потім визначаються причинно-наслідкові властивості і типи орбіт.
Mathematics Subject Classification: 53C30, 57S25.
Ключові слова:
кооднорідність один, простір Мінковського.Посилання
S. Adams and G. Stuck, The isometry group of a compact Lorentz manifold, I, Invent. Math. 129 (1997), No. 2, 239–261. https://doi.org/10.1007/s002220050163
S. Adams, Dynamics on Lorentz Manifolds, World Scientific Publishing Co., Inc., River Edge, NJ, 2001. https://doi.org/10.1142/4491
P. Ahmadi, Cohomogeneity one three dimensional anti-de Sitter space, proper and nonproper actions, Differential Geom. Appl. 39 (2015), 93–112. https://doi.org/10.1016/j.difgeo.2015.01.004
D.V. Alekseevskiı̆, On a proper action of Lie groups, Uspekhi Math. Nauk, 34 (1979), 219–220 (Russian). https://doi.org/10.1070/RM1979v034n01ABEH002875
A.V. Alekseevskiı̆ and D.V. Alekseevskiı̆, G-manifolds with one dimensional orbit space, Lie groups, their discrete subgroups, and invariant theory, Adv. Soviet Math., 8, Amer. Math. Soc., Providence, RI, 1992, 1–31. https://doi.org/10.1090/advsov/008/01
L. Berard-Bergery, Sur de nouvells variété riemanniennes d’Einstein, Inst. Élie Cartan 6 (1982), 1–60 (French).
G.E. Bredon, Introduction to Compact Transformation Groups. Pure and Applied Mathematics, 46, Academic Press, New York-London, 1972.
J.J. Duistermaat and J.A.C. Kolk, Lie Groups, Springer-Verlag, Berlin, 2000. https://doi.org/10.1007/978-3-642-56936-4
M. Hassani, On the irreducible action of PSL(2, R) on the 3-dimensional Einstein universe, C. R. Math. Acad. Sci. Paris, 355 (2017), 1133–1137. https://doi.org/10.1016/j.crma.2017.10.003
A.W. Knapp, Lie Groups Beyond an Introduction. 2nd edition. Progress in Mathematics, 140, Birkhäuser Boston, Inc., Boston, MA, 2002.
N. Kowalsky, Noncompact simple automorphism groups of Lorentz manifolds and other geometric manifolds, Ann. of Math. (2) 144 (1996), No. 3, 611–640. https://doi.org/10.2307/2118566
M.A. Magid, Lorentzian isoparametric hypersurfaces, Pacific J. Math. 118 (1985), No. 1, 165–197. https://doi.org/10.2140/pjm.1985.118.165
P.S. Mostert, On a compact Lie group acting on a manifold, Ann. of Math. (2) 65 (1957), No. 3, 447–455. https://doi.org/10.2307/1970056
R. Mirzaie and S.M.B. Kashani, On cohomogeneity one flat Riemannian manifolds, Glasg. Math. J. 44 (2002), 185–190. https://doi.org/10.1017/S0017089502020189
R.S. Palais and Ch.-L. Terng, A general theory of canonical forms, Trans. Amer. Math. Soc. 300 (1987), 771–789. https://doi.org/10.1090/S0002-9947-1987-0876478-4
R.S. Palais and Ch.-L. Terng, Critical Point Theory and Submanifold Geometry. Lecture Notes in Mathematics, 1353, Springer-Verlag, Berlin, 1988. https://doi.org/10.1007/BFb0087442
F. Podestà and A. Spiro, Some topological properties of chomogeneity one manifolds with negative curvature, Ann. Global Anal. Geom. 14 (1996), 69–79. https://doi.org/10.1007/BF00128196
C. Searle, Cohomogeneity and positive curvature in low dimension, Math. Z. 214 (1993), 491–498. https://doi.org/10.1007/BF02572419
J.C. Dı́az-Ramos, S.M.B. Kashani, and M.J. Vanaei, Cohomogeneity one actions on anti de Sitter spacetimes, Results Math. 72 (2017), No. 1-2, 515–536. https://doi.org/10.1007/s00025-017-0672-x
M.J. Vanaei, S.M.B. Kashani, and E. Straume, Cohomogeneity one anti de Sitter space AdS n+1 , Lobachevskii J. Math. 37 (2016), No. 2, 204–213. https://doi.org/10.1134/S1995080216020141
A. Zeghib, The identity component of the isometry group of a compact Lorentz manifold, Duke Math. J. 92 (1998), No. 2, 321–333. https://doi.org/10.1215/S0012-7094-98-09208-0
R.J. Zimmer, On the automorphism group of a compact Lorentz manifold and other geometric manifolds, Invent. Math. 83 (1986), 411–424. https://doi.org/10.1007/BF01394415
