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Geometry in a manifold with projective structure

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Abstract

Parallel transport of line elements, surface elements etc. along geodesics 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.

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References

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Authors and Affiliations

  1. Max-Planck Institut für Physik und Astrophysik, München, Germany

    J. Ehlers

  2. The University of Texas, Austin, Texas, USA

    A. Schild

Authors
  1. J. Ehlers
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  2. A. Schild
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Additional information

This paper is dedicated to our friend John Archibald Wheeler, geometer and physicist, who celebrated his sixtieth birthday on July 9, 1971.

This work was supported in part by the National Science Foundation (Grant No. GP-34639X). One of the authors (A.S.) did much of this work while visiting the Université Libre de Bruxelles (summer, 1968), Cambridge University (summer, 1970), and the Nordic Institute for Theoretical Atomic Physics (1970-71); he wishes to thank these institutions and Drs. I. Prigogine, D. Sciama, and C. Møller for their kind hospitality.

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Ehlers, J., Schild, A. Geometry in a manifold with projective structure. Commun.Math. Phys. 32, 119–146 (1973). https://doi.org/10.1007/BF01645651

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