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Differential Geometric Methods in Mathematical Physics pp 280–289Cite as

Jet bundles and weyl geometry

  • 4. Geometric methods and global analysis
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Part of the book series: Lecture Notes in Physics ((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)

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References

  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)

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  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 preparation

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  3. S. Kobayashi, Transformation Groups in Differential Geometry, Springer, New York, (1972) J. Dieudonné, Treatise on Analysis III, Academic Press, New York (1972)

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  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)

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  5. F.A.E. Pirani, A. Schild, in Perspectives in Geometry and General Relativity, (ed. B. Hoffmann), Bloomington (1966)

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  6. H. Weyl, Mathematische Analyse des Raumproblems

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Authors and Affiliations

  1. Institut für Theoretische Physik, Technische Universität Clausthal, D-3392, Clausthal

    J. D. Hennig

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  1. J. D. Hennig
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Heinz-Dietrich Doebner

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© 1981 Springer-Verlag

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Hennig, J.D. (1981). Jet bundles and weyl geometry. In: Doebner, HD. (eds) Differential Geometric Methods in Mathematical Physics. Lecture Notes in Physics, vol 139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10578-6_33

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  • DOI: https://doi.org/10.1007/3-540-10578-6_33

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10578-7

  • Online ISBN: 978-3-540-38573-8

  • eBook Packages: Springer Book Archive

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