On Holonomy and Homogeneous Spaces

Bertram Kostant

doi:10.1017/S0027763000021929

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In general a homogeneous space admits many invariant affine connections. Among these are certain connections which appear in many ways to be more natural than the others. We refer to the connections which K. Nomizu in [4] calls canonical affine connections of the first kind. When G is a compact connected Lie group and K a closed subgroup we called an invariant Riemannian metric on G/K, natural (in [2]) when it induced such a connection.

References

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[3] Kostant, B., On differential geometry and homogeneous spaces, II. Proc. Nat. Acad. Sci., vol. 42 (1956), pp. 354–357.Google Scholar

[4] Nomizu, K., Invariant affine connections on homogeneous spaces, Amer. Jour. Math., vol. 76 (1954), pp. 33–65.Google Scholar

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