THE INVERSION OF WHITEHEAD'S THEOREM ON CONVEX REGIONS

Lubom\' \i r Klapka

Abstract. In 1932 J. H. C. Whitehead [2] proved the
existence of convex neighbourhoods with respect to
the geodesic arcs corresponding to a given
connection on a manifold. The present paper gives necessary and sufficient
conditions for a set of paths to be the set of all geodesics of some
connection. The main condition is the existence of convex neighbourhoods
in a more general sense.

Keywords.  Linear connections, geodesics, convex regions.

MS classification.  53B05, 53C05, 53C22.