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Title: The integrability of a field of endomorphisms (English)
Author: Thompson, Gerard
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959
Volume: 127
Issue: 4
Year: 2002
Pages: 605-611
Summary lang: English
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Category: math
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Summary: A Theorem is proved that gives intrinsic necessary and sufficient conditions for the integrability of a zero-deformable field of endomorphisms. The Theorem is proved by reducing to a special case in which the endomorphism field is nilpotent. Many arguments used in the derivation of similar results are simplified, principally by means of using quotient rather than subspace constructions. (English)
Keyword: integrability
Keyword: endomorphism
Keyword: quotient space
MSC: 53A35
MSC: 53C10
MSC: 53C15
idZBL: Zbl 1015.53019
idMR: MR1942646
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Date available: 2009-09-24T22:05:50Z
Last updated: 2012-06-18
Stable URL: http://hdl.handle.net/10338.dmlcz/133948
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Reference: [1] E. T. Kobayashi: A remark on the Nijenhius tensor.Pacific J. Math. 12 (1961), 963–977.
Reference: [2] M. Kossowski, G. Thompson: Submersive second order ordinary differential equations.Math. Proc. Camb. Phil. Soc. 110 (1991), 207–224. MR 1104616
Reference: [3] J. Lehmann-Lejeune: Integrabilaté des $G$-structures définies par une 1-forme 0-déformable à valeurs dans le fibré tangent.Ann. Inst. Fourier 16 (1966), 329–387. MR 0212720
Reference: [4] F. J. Turiel: Intégrabilité d’un tenseur de type (1,1) et structure symplectique du fibré cotangent.C.R. Acad. Sci., Paris, Sér. I 301 (1985), 923–925. Zbl 0592.53024, MR 0829063
Reference: [5] F. J. Turiel: Classification locale d’un couple de formes symplectiques Poisson-compatible.C.R. Acad. Sci., Paris, t. 308, Série I (1989), 575–578. MR 1001810
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