On Immersions of m-Manifolds in (m+1)-Manifolds.
Let (P,ω) be a symplectic manifold. We find an integrability condition for an implicit differential system D' which is formed by a Lagrangian submanifold in the canonical symplectic tangent bundle (TP,ὡ).
Riemannian foliations constitute an important type of foliated structures. In this note we prove two theorems connecting the algebraic structure of Lie algebras of foliated vector fields with the smooth structure of a Riemannian foliation.
We prove that four manifolds diffeomorphic on the complement of a point have the same Donaldson invariants.
Necessary and sufficient conditions for the existence of -dimensional oriented vector bundles () over CW-complexes of dimension with prescribed Stiefel-Whitney classes , and Pontrjagin class are found. As a consequence some results on the span of 6 and 7-dimensional oriented vector bundles are given in terms of characteristic classes.