Differential properties of the sub-Riemannian distance function

• Autorzy: Grochowski M.
• Języki publikacji: EN

Abstrakty

EN

Let (M, H, g) be a sub-Riemannian manifold. Fix a point [p_0 belongs to M] and denote by f the sub-Riemannian distance from [p_0]. It is proved that f is smooth on an open and dense subset of a certain neighbourhood of a regular geodesic. On the other hand, each minimizing geodesic around which f is smooth is regular.

Słowa kluczowe

EN

distributions; geodesics; Riemannian metrics

PL

geodetyka; metryka Riemanna; rozkład

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2002
• Tom: Vol. 50, no 1
• Strony: 93--101
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Grochowski M.

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

Bibliografia

• [1] J. M. Bismut. Large deviations and the Malliavin calculus, Birkhäuser, Boston 1984.
• [2] W. Liu. H. J. Sussman, Shortest paths for sub-Riemannian metrics on rank-two distribution. Providence, November 1995.
• [3] R. Strichartz. Sub-Riemannian geometry, J. Differential Geom., 24 (1986) 221-263.