Rahula, Maido; Balan, Vladimir Tangent bundles and gauge groups. (English) Zbl 1351.58005 Uch. Zap. Kazan. Univ., Ser. Fiz.-Mat. Nauki 153, No. 3, 249-263 (2011). Let \(T^kM\) be the \(k\)th order iterated tangent bundle of an \(n\)-dimensional manifold \(M\). The authors show that the differentials \(T^ka\) of a diffeomorphism \(a\) of a smooth manifold \(M\) induce in the fibers of \(T^kM\) linear transformations, which embody the action of the \(k\)th order gauge group \(G_k\approx T^k(\mathrm{GL}(n,\mathbb R))\subset\mathrm{GL}(2^kn,\mathbb R)\). This action extends in a natural way to the osculating subbundles \(\mathrm{Osc}^{k-1}M\subset T^kM\). Reviewer: Miroslav Doupovec (Brno) MSC: 58A20 Jets in global analysis 58D17 Manifolds of metrics (especially Riemannian) Keywords:diffeomorphism of a smooth manifold; fiber bundles; action of the gauge group PDFBibTeX XMLCite \textit{M. Rahula} and \textit{V. Balan}, Uch. Zap. Kazan. Univ., Ser. Fiz.-Mat. Nauki 153, No. 3, 249--263 (2011; Zbl 1351.58005) Full Text: MNR