PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1997 | 41 | 1 | 11-20
Tytuł artykułu

Lorentzian geometry in the large

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Lorentzian geometry in the large has certain similarities and certain fundamental differences from Riemannian geometry in the large. The Morse index theory for timelike geodesics is quite similar to the corresponding theory for Riemannian manifolds. However, results on completeness for Lorentzian manifolds are quite different from the corresponding results for positive definite manifolds. A generalization of global hyperbolicity known as pseudoconvexity is described. It has important implications for geodesic structures.
Słowa kluczowe
Rocznik
Tom
41
Numer
1
Strony
11-20
Opis fizyczny
Daty
wydano
1997
Twórcy
autor
  • Mathematics Department, University of Missouri-Columbia, Columbia, MO 65211, U.S.A.
Bibliografia
  • [1] J. K. Beem and P. E. Ehrlich, Geodesic completeness and stability, Math. Proc. Camb. Phil. Soc. 102 (1987), 319-328.
  • [2] J. K. Beem, P. E. Ehrlich, and K. L. Easley, Global Lorentzian Geometry, Second Edition, Pure and Applied Math. Vol. 202, Marcel Dekker, New York, 1996.
  • [3] J. K. Beem and S. G. Harris, The generic condition is generic, Gen. Rel. and Grav. 25 (1993), 939-962.
  • [4] J. K. Beem and S. G. Harris, Nongeneric null vectors, Gen. Rel. and Grav. 25 (1993), 963-973.
  • [5] J. K. Beem, R. J. Low, and P. E. Parker, Spaces of geodesics: products, coverings, connectedeness, Geometriae Dedicata 59 (1996), 51-64.
  • [6] J. K. Beem and P. E. Parker, Pseudoconvexity and geodesic connectedness, Annali Math. Pura. Appl. 155 (1989), 137-142.
  • [7] J. K. Beem and P. E. Parker, Sectional curvature and tidal accelerations, J. Math. Phys. 31 (1990), 819-827.
  • [8] P. T. Chruściel, On Uniqueness in the Large of Solutions of Einstein Equations ('Strong Cosmic Censorship'), Australian University Press, Canberra, 1991.
  • [9] G. Galloway, The Lorentzian splitting theorem without completeness assumption, J. Diff. Geom. 29 (1989), 373-387.
  • [10] G. Galloway, The Lorentzian version of the Cheeger-Gromoll splitting theorem and its applications to General Relativity, in Differential Geometry: Geometry in Mathematical Physics and Related Topics, ed. R. Greene and S. -T. Yau, Amer. Math. Soc. Proceedings of Symposia in Pure Math., Vol. 54, Part 2 (1993), 249-257.
  • [11] D. Gromoll, W. Klingenberg and W. Meyer, Riemannsche Geometrie im Grossen, Lecture Notes in Math. Vol. 55, Springer-Verlag, Berlin, 1975.
  • [12] S. W. Hawking, G. F. R. Ellis, The Large Scale Structure of Space-time, Cambridge University Press, Cambridge, 1973
  • [13] N. J. Hicks, Notes on Differential Geometry, D. Van Nostrand, Princeton, New Jersey, 1965.
  • [14] H. Hopf and W. Rinow, Über den Begriff des vollständigen differentialgeometrischen Fläche, Comment. Math. Helv. 3 (1931), 209-225.
  • [15] S. Kobayashi, Riemannian manifolds without conjugate points, Ann. Math. Pura. Appl. 53 (1961), 149-155.
  • [16] A. Królak, Black holes and weak cosmic censorship, Gen. Rel. and Grav. 16 (1984), 365-373.
  • [17] A. Królak and W. Rudnicki, Singularities, trapped sets, and cosmic censorship in asymptotically flat space-times, International J. Theoret. Phys. 32 (1993), 137-142.
  • [18] B. Mashhoon, Tidal radiation, Astrophys. J. 216 (1977), 591-609.
  • [19] B. Mashhoon and J. C. McClune, Relativistic tidal impulse, Month. Notices Royal Astron. Soc. 262 (1993), 881-888.
  • [20] R. P. A. C. Newman, A proof of the splitting conjecture of S.-T. Yau, J. Diff. Geom. 31 (1990), 163-184.
  • [21] B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity, Pure and Applied Math. Vol. 103, Academic Press, New York, 1983.
  • [22] H. -J. Seifert, Global connectivity by timelike geodesics, Zs. f. Naturforsche 22a (1967), 1356-1360.
  • [23] P. M. Williams, Completeness and its stability on manifolds with connection, Ph.D. Thesis, Dept. Math. Univ. of Lancaster, 1984.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv41z1p11bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.