Open Access
April, 2016 Milnor-type theorems for left-invariant Riemannian metrics on Lie groups
Takahiro HASHINAGA, Hiroshi TAMARU, Kazuhiro TERADA
J. Math. Soc. Japan 68(2): 669-684 (April, 2016). DOI: 10.2969/jmsj/06820669


For all left-invariant Riemannian metrics on three-dimensional unimodular Lie groups, there exist particular left-invariant orthonormal frames, so-called Milnor frames. In this paper, for any left-invariant Riemannian metrics on any Lie groups, we give a procedure to obtain an analogous of Milnor frames, in the sense that the bracket relations among them can be written with relatively smaller number of parameters. Our procedure is based on the moduli space of left-invariant Riemannian metrics. Some explicit examples of such frames and applications will also be given.


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Takahiro HASHINAGA. Hiroshi TAMARU. Kazuhiro TERADA. "Milnor-type theorems for left-invariant Riemannian metrics on Lie groups." J. Math. Soc. Japan 68 (2) 669 - 684, April, 2016.


Published: April, 2016
First available in Project Euclid: 15 April 2016

zbMATH: 1353.53058
MathSciNet: MR3488140
Digital Object Identifier: 10.2969/jmsj/06820669

Primary: 53C25 , 53C30

Keywords: left-invariant Riemannian metrics , Lie groups , Milnor frames , Milnor-type theorems , Ricci signatures , solvsolitons

Rights: Copyright © 2016 Mathematical Society of Japan

Vol.68 • No. 2 • April, 2016
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