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On Holonomy and Homogeneous Spaces

Published online by Cambridge University Press:  22 January 2016

Bertram Kostant
Bertram Kostant*
Affiliation:
Berkeley, California
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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.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 12 , December 1957, pp. 31 - 54
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1957

References

[1] Kostant, B., Holonomy and the Lie algebra of infinitesimal motions of a Riemannian manifold, Trans. Amer. Math. Soc, vol. 80 (1955), pp. 528–542.Google Scholar
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