Affine transformations of a transversal projectable connection on a foliated manifold

Consider the principal bundle of quotient-frames on a foliated manifold. This paper gives, and supplements, results about canonical, transversal and projectable forms, about foliated vector fields and their natural lifts, and about lifted foliations. The basic cross-sections of a transversal connection are introduced and studied. Criteria for transversality and projectability of connections in the quotient-frame bundle are established, and it is shown that the quotient Lie algebra consisting of the infinitesimal affine transformations of a projectable connection is finite-dimensional, and that so is the quotient Lie group consisting of affine transformations of a transversally-complete, projectable connection on a manifold with a transversally orientable foliation having a closed leaf.
Bibliography: 19 titles.