Holomorphic non-holonomic differential systems on complex manifolds

S. Dimiev
1991 Annales Polonici Mathematici  
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. 1991 Mathematics Subject Classification: Primary 32B99, 32L05. Key words and phrases: holomorphic tangent sheaf, D-stable ideal,
more » ... -stable ideal, power D-expansion, involutive completion. S. Dimiev We also recall that a complex space X is called a closed complex subspace of M if there is a coherent ideal I of O M , I ⊂ O M , such that X = supp(O M /I) and O x = (O M /I)|X. In this case there is a canonical holomorphic map determined by the injection and denoted by X ⊂ M . The tangent space of X, denoted by T X, is defined as usual [1] . If G is an open subset of M and O G is the induced structure sheaf, we assume that the ideal
doi:10.4064/ap-55-1-65-73 fatcat:ffaa6gai6jcedmzvbfpilptloi