Homogeneous spaces with invariant projectively flat affine connections

Shima, Hirohiko

doi:10.1090/S0002-9947-99-02523-4

Homogeneous spaces with invariant projectively flat affine connections
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by Hirohiko Shima

Trans. Amer. Math. Soc. 351 (1999), 4713-4726

DOI: https://doi.org/10.1090/S0002-9947-99-02523-4

Published electronically: August 25, 1999

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Abstract:

We characterize invariant projectively flat affine connections in terms of affine representations of Lie algebras, and show that a homogeneous space admits an invariant projectively flat affine connection if and only if it has an equivariant centro-affine immersion. We give a correspondence between semi-simple symmetric spaces with invariant projectively flat affine connections and central-simple Jordan algebras.

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