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Journal Article

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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335144.pdf
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Citation

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


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-5EDF-E
Abstract
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.