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

zbMath1345.53073arXiv1412.4565MaRDI QIDQ2811555

Donato Pertici, Alberto Dolcetti

Publication date: 10 June 2016

Full work available at URL: https://arxiv.org/abs/1412.4565

zbMATH Keywords

geodesicssemi-Riemannian manifoldstrace metriccurvature tensorsexponential and logarithm of real matricesnonsingular (special) matrices

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Matrix exponential and similar functions of matrices (15A16)

Related Items (5)

Skew symmetric logarithms and geodesics on \(\mathrm{O}_n(\mathbb{R})\) ⋮ Geometry of logarithmic strain measures in solid mechanics ⋮ The full group of isometries of some compact Lie groups endowed with a bi-invariant metric ⋮ Elliptic isometries of the manifold of positive definite real matrices with the trace metric ⋮ Optimization on the real symplectic group

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