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

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arxiv 1412.4565 v1 pith:XFFDHS54 submitted 2014-12-15 math.DG

Alberto Dolcetti , Donato Pertici This is my paper · ORCID
classification math.DG
keywords mathbbisometricmetricpropertiessemi-riemanniansometracecomponent
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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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  1. A data-based notion of quantiles on Hadamard spaces

    stat.ME 2025-06 conditional novelty 5.0 of 10

    A data-based geometric quantile loss on Hadamard spaces is defined and shown to improve on parameter-based quantiles in consistency, asymptotic normality, robustness, extreme behavior, and computability.

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