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Relating Thomas-Whitehead Projective Connections by a Gauge Transformation

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Abstract

Thomas-Whitehead projective connections, or TW-connections, are torsionfree linear connections, satisfying certain properties, on a naturally defined principal R-bundle over a manifold. The name credits T. Y. Thomas and J. H. C. Whitehead, who originally studied these connections in the 1920's and 1930's. Three equivalence classes of TW-connections will be considered. This leads to a necessary and sufficient condition for TW-connections to be related by a gauge transformation; namely, they induce the same projective structure on the base manifold, have identical Ricci tensor, and induce the identity element in the one-dimensional de Rham cohomology vector space of the base manifold.

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Authors and Affiliations

  1. Department of Mathematics, Southeast Missouri State University, Cape Girardeau, MO 63701-4799, U.S.A

    Craig Roberts

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  1. Craig Roberts
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Roberts, C. Relating Thomas-Whitehead Projective Connections by a Gauge Transformation. Mathematical Physics, Analysis and Geometry 7, 1–8 (2004). https://doi.org/10.1023/B:MPAG.0000022829.24539.ed

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  • DOI: https://doi.org/10.1023/B:MPAG.0000022829.24539.ed

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