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Manuscripta Mathematica

, Volume 135, Issue 1–2, pp 229–243 | Cite as

The space of left-invariant metrics on a Lie group up to isometry and scaling

  • Hiroshi Kodama
  • Atsushi Takahara
  • Hiroshi TamaruEmail author
Article

Abstract

We study the spaces of left-invariant Riemannian metrics on a Lie group up to isometry, and up to isometry and scaling. In this paper, we see that such spaces can be identified with the orbit spaces of certain isometric actions on noncompact symmetric spaces. We also study some Lie groups whose spaces of left-invariant metrics up to isometry and scaling are small.

Mathematics Subject Classification (2000)

53C30 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Hiroshi Kodama
    • 1
    • 2
  • Atsushi Takahara
    • 1
    • 3
  • Hiroshi Tamaru
    • 1
    Email author
  1. 1.Department of MathematicsHiroshima UniversityHigashi-HiroshimaJapan
  2. 2.System Be-Alpha Inc.FukuokaJapan
  3. 3.Saga Technical High SchoolSagaJapan

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