Distributions on spray spaces (Q2770036)

One considers a manifold \(M\) with a regular distribution \(D\) and a spray \(S\) on \(TM\). The projections of the integral curves of \(S\) on \(M\) are called geodesics. \(D\) is said to be geodesically invariant \((g.i.)\) if for any geodesic whose initial tangent, vector is in \(D\) it follows that all its tangent, vectors belong to \(D\). A characterization of g.i. distributions is given using the Berwald connection associated to \(S\). This is applied to some distributions on \(TM\).NEWLINENEWLINENEWLINE(Misprints: In (2.2) \(\widehat D_X\), \(\widehat D_Y\) are \(\widehat D_{X^h},\widehat D_{Y^h}\); \(D_XY\) is \(\widehat D_{X^h}y)\).