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On the Geodesics of a Manifold Having a Linear Connection
Author(s) -
Williams Gareth
Publication year - 1974
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-9.1.118
Subject(s) - mathematics , manifold (fluid mechanics) , topology (electrical circuits) , geodesic , connection (principal bundle) , pure mathematics , closed manifold , real projective space , projective space , invariant manifold , complex projective space , mathematical analysis , projective test , combinatorics , geometry , mechanical engineering , engineering
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 C 1 on the geodesies are the projective mappings, and thus give a representation of the projective group of the manifold.