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The space of left-invariant metrics on a Lie group up to isometry and scaling |
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| Authors: | Hiroshi Kodama Atsushi Takahara Hiroshi Tamaru |
| Affiliation: | 1. Department of Mathematics, Hiroshima University, Higashi-Hiroshima, 739-8526, Japan 2. System Be-Alpha Inc., Fukuoka, 810-0022, Japan 3. Saga Technical High School, Saga, 840-0841, Japan |
| 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. |
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