Homogeneous structures on manifolds: Differential geometry from the point of view of differential equations
Let \(N\) be a manifold together with a transitive action of the Lie group \(G\) and \(M\) be any smooth manifold with \(\dim M= \dim N\). The author calls a free \((N,G)\)-coframe of order \(k\) at a point \(x\in M\) the \(k\)-jet of a local diffeomorphism \(\varphi: M\to N\) at this point and denotes by \(R^ k (M)\) the space of all free \(k\)-coframes. The Lie group \(G\) acts in a natural way in the fiber bundle of free coframes. By a homogeneous \((N,G)\)-structure on a manifold \(M\) he means a subbundle \(E_ k\subset R^ k(M)\) which is the principal \(G\)-bundle with respect to the action of the group \(G\) in the space \(R^ k(M)\). In the paper under review, the author considers some properties of such structures related to systems of differential equations, Cartan connection and its curvature.
symbol of the system of differential equations
scientific article; zbMATH DE number 484282