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arXiv · 1412.4565

Some differential properties of $GL_n(\mathbb{R})$ with the trace metric

Alberto Dolcetti·Donato Pertici
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Abstract

In this note we consider some properties of $GL_n(\mathbb{R})$ with the Semi-Riemannian structure induced by the trace metric $g$. In particular we study geodesics and curvature tensors. Moreover we prove that $GL_n$ has a suitable foliation, whose leaves are isometric to $(SL_n(\mathbb{R}), g)$, while its component of matrices with positive determinant is isometric to the Semi-Riemannian product manifold $SL_n \times \mathbb{R}$.

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Alberto Dolcetti, Donato Pertici. 2014-12-15. Some differential properties of $GL_n(\mathbb{R})$ with the trace metric. https://arxiv.org/abs/1412.4565

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