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.
@article{bwmeta1.element.bwnjournal-article-apmv55z1p65bwm,
author = {S. Dimiev},
title = {Holomorphic non-holonomic differential systems on complex manifolds},
journal = {Annales Polonici Mathematici},
volume = {55},
year = {1991},
pages = {65-73},
zbl = {0759.32006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv55z1p65bwm}
}
S. Dimiev. Holomorphic non-holonomic differential systems on complex manifolds. Annales Polonici Mathematici, Tome 55 (1991) pp. 65-73. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv55z1p65bwm/
[000] [1] S. Fischer, Complex Analytic Geometry, Lecture Notes in Math. 538, Springer, 1976. | Zbl 0343.32002
[001] [2] H. Grauert and R. Remmert, Coherent Analytic Sheaves, Springer, 1984.
[002] [3] A. M. Vershik and V. Ya. Gershkovich, Nonholonomic dynamical systems. Geometry of distributions and variational problems, in: Sovrem. Probl. Mat. Fund. Napravl. 16, VINITI, Moscow 1987, 5-85 (in Russian). | Zbl 0797.58007