Geometry in a manifold with projective structure

Ehlers, Jürgen; Schild, A.

doi:10.1007/BF01645651

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Geometry in a manifold with projective structure

MPS-Authors

Ehlers, Jürgen
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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引用

Ehlers, J., & Schild, A. (1973). Geometry in a manifold with projective structure. Communications in Mathematical Physics, 32(2), 119-146. doi:10.1007/BF01645651.

引用: https://hdl.handle.net/11858/00-001M-0000-0013-5EDF-E

要旨

Parallel transport of line elements, surface elements etc. along geodesies and more general curves in a projectively connected manifold is investigated analytically and in terms of geometrical constructions. Projective curvature is characterized geometrically by a projective analogue of the geodesic deviation equation and by a geometrical construction. The results are interpreted physically as statements about free fall world lines in space-time.