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Jet bundles and weyl geometry

  • J. D. Hennig
4. Geometric methods and global analysis
Part of the Lecture Notes in Physics book series (LNP, volume 139)

Abstract

Describing the projective structure P (given by the set of “freely falling particles”) and the conformal (light cone) structure ℂ of space time via subbundles of second order frame bundles, we investigate the existence and uniqueness of a Weyl geometry compatible with P and ℂ

We first review some basic notions concerning the fibre bundle description of geometric structures on differentiable manifolds and then apply this formalism to the central step in the axiomatic approach to space time geometry presented by Ehiers, Pirani and Schild in (1). For a more detailed version of our lecture, cf. (2)

Keywords

Conformal Structure Projective Structure Isotropy Subgroup Linear Connection Space Time Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. (1).
    J. Ehlers, F.A.E. Pirani, A. Schild, in General Relativity (ed. L. O'Raifeartaigh, Oxford (1972) F.A.E. Pirani, Symposia Mathematica XII, 119, 67 (1973) J. Ehlers, in Relativity, Astrophysics and Cosmology, (ed. W. Israel), D. Reidel, Dordrecht-Holland (1973)Google Scholar
  2. (2).
    J.D. Hennig, G-structures and Space Time Geometry I, ICTP, Trieste, preprint IC/78/46, and G-Structures and Space Time Geometry II, in preparationGoogle Scholar
  3. (3).
    S. Kobayashi, Transformation Groups in Differential Geometry, Springer, New York, (1972) J. Dieudonné, Treatise on Analysis III, Academic Press, New York (1972)Google Scholar
  4. (4).
    S. Kobayashi, K. Nomizu, Foundations of Differential Geometry I, Interscience, New York (1963) Greub, S. Halperin, R. Vanstone, Connections, Curvature and Cohomology II, Academic Press, New York (1973)Google Scholar
  5. (5).
    F.A.E. Pirani, A. Schild, in Perspectives in Geometry and General Relativity, (ed. B. Hoffmann), Bloomington (1966)Google Scholar
  6. (6).
    H. Weyl, Mathematische Analyse des RaumproblemsGoogle Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • J. D. Hennig
    • 1
  1. 1.Institut für Theoretische PhysikTechnische Universität ClausthalClausthal

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