On Holonomy and Homogeneous Spaces
- 1 December 1957
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 12, 31-54
- https://doi.org/10.1017/s0027763000021929
Abstract
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.Keywords
This publication has 5 references indexed in Scilit:
- Some Studies on Kaehlerian Homogeneous SpacesNagoya Mathematical Journal, 1957
- ON DIFFERENTIAL GEOMETRY AND HOMOGENEOUS SPACES. IIProceedings of the National Academy of Sciences, 1956
- ON DIFFERENTIAL GEOMETRY AND HOMOGENEOUS SPACES. IProceedings of the National Academy of Sciences, 1956
- Holonomy and the Lie algebra of infinitesimal motions of a Riemannian manifoldTransactions of the American Mathematical Society, 1955
- Invariant Affine Connections on Homogeneous SpacesAmerican Journal of Mathematics, 1954