Holomorphic non-holonomic differential systems on complex manifolds

S. Dimiev

Annales Polonici Mathematici (1991)

  • Volume: 55, Issue: 1, page 65-73
  • ISSN: 0066-2216

Abstract

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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 [3] which is related with some problems of mechanics.

How to cite

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S. Dimiev. "Holomorphic non-holonomic differential systems on complex manifolds." Annales Polonici Mathematici 55.1 (1991): 65-73. <http://eudml.org/doc/262511>.

@article{S1991,
abstract = {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.},
author = {S. Dimiev},
journal = {Annales Polonici Mathematici},
keywords = {holomorphic tangent sheaf; 𝓓-stable ideal; power 𝓓-expansion; involutive completion},
language = {eng},
number = {1},
pages = {65-73},
title = {Holomorphic non-holonomic differential systems on complex manifolds},
url = {http://eudml.org/doc/262511},
volume = {55},
year = {1991},
}

TY - JOUR
AU - S. Dimiev
TI - Holomorphic non-holonomic differential systems on complex manifolds
JO - Annales Polonici Mathematici
PY - 1991
VL - 55
IS - 1
SP - 65
EP - 73
AB - 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.
LA - eng
KW - holomorphic tangent sheaf; 𝓓-stable ideal; power 𝓓-expansion; involutive completion
UR - http://eudml.org/doc/262511
ER -

References

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  1. [1] S. Fischer, Complex Analytic Geometry, Lecture Notes in Math. 538, Springer, 1976. Zbl0343.32002
  2. [2] H. Grauert and R. Remmert, Coherent Analytic Sheaves, Springer, 1984. 
  3. [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). Zbl0797.58007

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