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November 2016 On the moduli spaces of left-invariant pseudo-Riemannian metrics on Lie groups
Akira Kubo, Kensuke Onda, Yuichiro Taketomi, Hiroshi Tamaru
Hiroshima Math. J. 46(3): 357-374 (November 2016). DOI: 10.32917/hmj/1487991627

Abstract

The moduli space of left-invariant pseudo-Riemannian metrics on a given Lie group is defined as the orbit space of a certain isometric action on some pseudo- Riemannian symmetric space. In terms of the moduli space, we formulate a procedure to obtain a generalization of Milnor frames for left-invariant pseudo-Riemannian metrics on a given Lie group. This procedure is an analogue of the recent studies on left-invariant Riemannian metrics. In this paper, we describe the orbit space of the action of a particular parabolic subgroup, and then apply it to obtain a generalization of Milnor frames for so-called the Lie groups of real hyperbolic spaces, and also for the three-dimensional Heisenberg group. As a corollary we show that all left-invariant pseudo-Riemannian metrics of arbitrary signature on the Lie groups of real hyperbolic spaces have constant sectional curvatures.

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Akira Kubo. Kensuke Onda. Yuichiro Taketomi. Hiroshi Tamaru. "On the moduli spaces of left-invariant pseudo-Riemannian metrics on Lie groups." Hiroshima Math. J. 46 (3) 357 - 374, November 2016. https://doi.org/10.32917/hmj/1487991627

Information

Received: 19 November 2015; Revised: 22 January 2016; Published: November 2016
First available in Project Euclid: 25 February 2017

zbMATH: 1360.53029
MathSciNet: MR3614303
Digital Object Identifier: 10.32917/hmj/1487991627

Subjects:
Primary: 53B30, 53C30

Rights: Copyright © 2016 Hiroshima University, Mathematics Program

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Vol.46 • No. 3 • November 2016
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