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Journal of the London Mathematical Society 1974 s2-9(1):118-120; doi:10.1112/jlms/s2-9.1.118
© 1974 by London Mathematical Society
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© Oxford University Press

On the Geodesics of a Manifold Having a Linear Connection

Gareth Williams

Department of Mathematics, Stetson University Deland, Florida 32720, U.S.A.

A fine topology is introduced on a manifold. The topology is such that homeomorphisms from the unit closed interval into the fine topological space define the geodesies. Thus the geodetic structure of the manifold is represented by a fine topological structure. It is shown that the group of homeomorphisms of the manifold is the group of piecewise projective mappings; the homeomorphisms that are C1 on the geodesies are the projective mappings, and thus give a representation of the projective group of the manifold.


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