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arXiv · 1509.08336

On the moduli spaces of left-invariant pseudo-Riemannian metrics on Lie groups

Akira Kubo·Kensuke Onda·Yuichiro Taketomi·Hiroshi Tamaru
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Abstract

In this paper, 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, and is based on the moduli space of left-invariant pseudo-Riemannian metrics. As one of applications, we show that any 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. 2015-09-28. On the moduli spaces of left-invariant pseudo-Riemannian metrics on Lie groups. https://arxiv.org/abs/1509.08336

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