On submaximal dimension of the group of almost isometries of Finsler metrics

zbMATH Open1339.53071arXiv1207.6922MaRDI QIDQ2786833

Vladimir S. Matveev

Publication date: 23 February 2016

Abstract: We show that the second greatest possible dimension of the group of (local) almost isometries of a Finsler metric is $frac{n}^2-n2+1$ for $n=dim(M)e4$ and $frac{n}^2-n2+2=8$ for $n=4$. If a Finsler metric has the group of almost isometries of dimension greater than $frac{n}^2-n2+1$, then the Finsler metric is Randers, i.e., $F(x,y)=sqrt{g}_x(y,y)+au(y)$. Moreover, if $ne4$, the Riemannian metric $g$ has constant sectional curvature and, if in addition $ne2$, the 1-form $au$ is closed, so (locally) the metric admits the group of local isometries of the maximal dimension $fracn(n+1)2$.

Full work available at URL: https://arxiv.org/abs/1207.6922

zbMATH Keywords

Randers metricalmost isometryalmost Killing vector fieldgroup of almost isometries

Mathematics Subject Classification ID

Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60) Local differential geometry of Finsler spaces and generalizations (areal metrics) (53B40)

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