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Naturally Reductive Homogeneous Riemannian Manifolds

Published online by Cambridge University Press:  20 November 2018

Carolyn S. Gordon
Carolyn S. Gordon*
Affiliation:
Washington University, St. Louis, Missouri
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The simple algebraic and geometric properties of naturally reductive metrics make them useful as examples in the study of homogeneous Riemannian manifolds. (See for example [2], [3], [15]). The existence and abundance of naturally reductive left-invariant metrics on a Lie group G or homogeneous space G/L reflect the structure of G itself. Such metrics abound on compact groups, exist but are more restricted on noncompact semisimple groups, and are relatively rare on solvable groups. The goals of this paper are

  • (i) to study all naturally reductive homogeneous spaces of G when G is either semisimple of noncompact type or nilpotent and

  • (ii) to give necessary conditions on a Riemannian homogeneous space of an arbitrary Lie group G in order that the metric be naturally reductive with respect to some transitive subgroup of G.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 37 , Issue 3 , 01 June 1985 , pp. 467 - 487
Copyright
Copyright © Canadian Mathematical Society 1985

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