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On implicit Lagrangian differential systems

S. Janeczko (2000)

Annales Polonici Mathematici

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).

On Lie algebras of vector fields related to Riemannian foliations

Tomasz Rybicki (1993)

Annales Polonici Mathematici

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.

On manifolds diffeomorphic on the complement of a point

Stefano De Michelis (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We prove that four manifolds diffeomorphic on the complement of a point have the same Donaldson invariants.

On oriented vector bundles over CW-complexes of dimension 6 and 7

Martin Čadek, Jiří Vanžura (1992)

Commentationes Mathematicae Universitatis Carolinae

Necessary and sufficient conditions for the existence of n -dimensional oriented vector bundles ( n = 3 , 4 , 5 ) over CW-complexes of dimension 7 with prescribed Stiefel-Whitney classes w 2 = 0 , w 4 and Pontrjagin class p 1 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.

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