Skip to main content
Top

2013 | OriginalPaper | Chapter

On the Isometry Group of Lorentz Manifolds

Authors : Leandro A. Lichtenfelz, Paolo Piccione, Abdelghani Zeghib

Published in: Recent Trends in Lorentzian Geometry

Publisher: Springer New York

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We will first review a construction in [10] to establish the Lie group structure of the group of isometries of a semi-Riemannian manifold. The problem is cast in the language of G-structures. In the second part of this chapter, we will review some recent results on the classification of groups acting isometrically on compact Lorentz manifolds and on the geometry of compact manifolds whose isometry group is non compact.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Adams, S., Stuck, G.: The isometry group of a compact Lorentz manifold. I, II. Invent. Math. 129(2), 239–261, 263–287 (1997) Adams, S., Stuck, G.: The isometry group of a compact Lorentz manifold. I, II. Invent. Math. 129(2), 239–261, 263–287 (1997)
3.
go back to reference Gromov, M.: Rigid transformations groups. Géométrie différentielle (Paris, 1986), 65–139, Travaux en Cours, 33, Hermann, Paris (1988) Gromov, M.: Rigid transformations groups. Géométrie différentielle (Paris, 1986), 65–139, Travaux en Cours, 33, Hermann, Paris (1988)
4.
go back to reference Kowalsky, N.: Noncompact simple automorphism groups of Lorentz manifolds and other geometric manifolds. Ann. of Math. (2) 144(3), 611–640 (1996) Kowalsky, N.: Noncompact simple automorphism groups of Lorentz manifolds and other geometric manifolds. Ann. of Math. (2) 144(3), 611–640 (1996)
6.
go back to reference Myers, S.B., Steenrod, N.: The group of isometries of a Riemannian manifold. Ann. of Math. 40(400–416) (1939) Myers, S.B., Steenrod, N.: The group of isometries of a Riemannian manifold. Ann. of Math. 40(400–416) (1939)
7.
go back to reference Newlander, A., Nirenberg, L.: Complex analytic coordinates in almost complex manifolds. Ann. of Math. (2) (65), (1957) Newlander, A., Nirenberg, L.: Complex analytic coordinates in almost complex manifolds. Ann. of Math. (2) (65), (1957)
8.
go back to reference Ogiue, K.: Theory of conformal connections. Kodai Math. Sem. Rep. 19(193–224) (1967) Ogiue, K.: Theory of conformal connections. Kodai Math. Sem. Rep. 19(193–224) (1967)
9.
go back to reference Piccione P., Zeghib, A.: On the isometry group and the geometric structure of compact stationary Lorentzian manifolds, preprint (2010) arXiv:1002.0814. Piccione P., Zeghib, A.: On the isometry group and the geometric structure of compact stationary Lorentzian manifolds, preprint (2010) arXiv:1002.0814.
10.
go back to reference Sternberg, S.: Lectures on Differential Geometry. Prentice-Hall, Englewood Cliffs (1964)MATH Sternberg, S.: Lectures on Differential Geometry. Prentice-Hall, Englewood Cliffs (1964)MATH
11.
go back to reference Zeghib, A.: Sur les espaces-temps homogènes. The Epstein birthday schrift, pp. 551–576 (electronic), Geom. Topol. Monogr., vol. 1. Geom. Topol. Publ., Coventry (1998) Zeghib, A.: Sur les espaces-temps homogènes. The Epstein birthday schrift, pp. 551–576 (electronic), Geom. Topol. Monogr., vol. 1. Geom. Topol. Publ., Coventry (1998)
12.
go back to reference Zimmer, R. J.: On the automorphism group of a compact Lorentz manifold and other geometric manifolds. Invent. Math. 83(3), 411–424 (1986)MathSciNetMATHCrossRef Zimmer, R. J.: On the automorphism group of a compact Lorentz manifold and other geometric manifolds. Invent. Math. 83(3), 411–424 (1986)MathSciNetMATHCrossRef
Metadata
Title
On the Isometry Group of Lorentz Manifolds
Authors
Leandro A. Lichtenfelz
Paolo Piccione
Abdelghani Zeghib
Copyright Year
2013
Publisher
Springer New York
DOI
https://doi.org/10.1007/978-1-4614-4897-6_12

Premium Partner