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Natural transformations of symmetric affine connections on manifolds to metrics on linear frame bundles: a classification

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Abstract

We find all second order natural transformations of symmetric affine connections on manifolds into metrics on linear frame bundles. The complete family of naturally resulting metrics (to a fixed symmetric affine connection) is a real vector space generated by some generalization of two “classical” liftings.

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Authors and Affiliations

  1. Department of Mathematics, Tokyo Gakugei University, Koganei-Shi Nukuikita-Machi 4-1-1, 184, Tokyo, Japan

    Masami Sekizawa

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  1. Masami Sekizawa
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Sekizawa, M. Natural transformations of symmetric affine connections on manifolds to metrics on linear frame bundles: a classification. Monatshefte für Mathematik 105, 229–243 (1988). https://doi.org/10.1007/BF01636931

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  • DOI: https://doi.org/10.1007/BF01636931

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