| Title:
|
The integrability of a field of endomorphisms (English) |
| Author:
|
Thompson, Gerard |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
127 |
| Issue:
|
4 |
| Year:
|
2002 |
| Pages:
|
605-611 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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 |
| DOI:
|
10.21136/MB.2002.133948 |
| . |
| Date available:
|
2009-09-24T22:05:50Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133948 |
| . |
| 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, 10.1017/S0305004100070262 |
| 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, 10.5802/aif.246 |
| 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 |
| . |
