We study coherent subsheaves 𝓓 of the holomorphic tangent sheaf of a complex manifold. A description of the corresponding 𝓓-stable ideals and their closed complex subspaces is sketched. Our study of non-holonomicity is based on the Noetherian property of coherent analytic sheaves. This is inspired by the paper [3] which is related with some problems of mechanics.
Soit un germe en de 1-forme différentielle holomorphe, satisfaisant la condition d’intégrabilité et non dicritique, i.e. sur toute surface non intégrale de , on ne peut tracer, au voisinage de 0, qu’un nombre fini de germes de courbes analytiques , intégrales de , avec . Alors possède un germe d’hypersurface analytique intégrale.
Let X be a differentiable manifold endowed with a transitive action α: A×X→X of a Lie group A. Let K be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms of explicit finite dimensional quotients, of three classes of objects: equivalence classes of α-invariant K-connections on X α-invariant gauge classes of K-connections on X, andα-invariant isomorphism classes of pairs (Q,P) consisting of a holomorphic Kℂ-bundle Q → X and a K-reduction P of Q (when...
Soit un fibré holomorphe localement trivial de base une variété de Stein et de fibre une courbe compacte.Si est un ouvert localement pseudoconvexe de ne contenant aucune fibre, alors est de Stein.
We generalize a theorem of Siciak on the polynomial approximation of the Lelong class to the setting of toric manifolds with an ample line bundle. We also characterize Lelong classes by means of a growth condition on toric manifolds with an ample line bundle and construct an example of a nonample line bundle for which Siciak's theorem does not hold.