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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  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,doi:10.4064/ap-55-1-65-73 fatcat:ffaa6gai6jcedmzvbfpilptloi