Path structures on manifolds
- 1 October 1977
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 18 (10) , 2014-2018
- https://doi.org/10.1063/1.523175
Abstract
We study collections of paths—i.e., unparametrized curves—on a manifold such that through every point and every direction at that point there passes exactly one path. Among such path structures we characterize, analytically and in terms of symmetries, those which consist of geodesics of a linear connection. Examples of nongeodesic path structures are given, and some of the results are interpreted physically. Journal of Mathematical Physics is copyrighted by The American Institute of PhysicsKeywords
This publication has 5 references indexed in Scilit:
- Geometry in a manifold with projective structureCommunications in Mathematical Physics, 1973
- The differentiable and causal structures of space-timeJournal of Mathematical Physics, 1973
- The Riemannian Structure of Space-Time as a Consequence of a Measurement MethodJournal of Mathematical Physics, 1971
- Causal structure in space-timeGeneral Relativity and Gravitation, 1971
- On the structure of causal spacesMathematical Proceedings of the Cambridge Philosophical Society, 1967