Geodesics in the sub-Lorentzian geometry

• Autorzy: Grochowski M.
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to introduce the notion of sub-Lorentzian manifolds (which is done by analogy to sub-Riemannian manifolds) and to describe basic properties of such manifolds. In particular, we investigate problems related to the existence of the longest curves between two given points, and examine some conditions for continuity and differentiability of the (local) sub-Lorentzian distance function.

Słowa kluczowe

EN

distributions; geodesics; Lorentzian manifolds

PL

dystrybucja; geodetyka; rozmaitość Lorentza

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2002
• Tom: Vol. 50, no 2
• Strony: 161--178
• Opis fizyczny: Bibliogr. 5 egz.

Twórcy

autor

Grochowski M.

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland,

Bibliografia

• [1] J. K. Beem, P. E. Ehrlich, K. L. Easley, Global Lorentzian geometry, Marcel Dekker, 1996.
• [2] J.-M. Bismut, Large deviations and the Malliavin calculus, Birkhäuser, Boston 1984.
• [3] M. Grochowski, Differential properties of the sub-Riemannian distance function, Bull. Pol. Ac.: Math., 50 (1) (2002) 93-101.
• [4] W. Liu, H. J. Sussman, Shortest paths for sub-Riemannian metrics on rank-two distribution, Providence, November 1995.
• [5] R. Penrose, Techniques of differential topology in relativity, Regional Conference Series in Applied Math. 7, SIAM. Philadelphia 1972.