|
The integrability problem for Lie equations
Author(s):
Hubert
Goldschmidt
Journal:
Bull. Amer. Math. Soc.
84
(1978),
531-546.
MSC (1970):
Primary 58H05, 22E65, 58G99, 35N10, 53C10
MathSciNet review:
0517116
Retrieve article in:
PDF
References |
Similar articles |
Additional information
References:
- 1.
- C. Buttin and P. Molino, Théorème général d'équivalence pour les pseudogroupes de Lie plats transitifs, J. Differential Geometry 9 (1972), 347-354. MR 353382
- 2.
- É. Cartan, Sur la structure des groupes infinis de transformations, Ann. Sci. École Norm. Sup. 21 (1904), 153-206; 22 (1905), 219-308; Oeuvres complètes: II, vol. 2, Groupes infinis, systèmes différentiels, théories d'équivalence, Gauthier-Villars, Paris, 1953, pp. 571-714.
- 3.
- É. Cartan, La structure des groupes infinis, Oeuvres complètes: II, vol. 2, Gauthier-Villars, Paris, 1953, pp. 1335-1384. MR 58523
- 4.
- J. F. Conn, A new class of counterexamples to the integrability problem, Proc. Nat. Acad. Sci. U.S.A. 74 (1977), 2655-2658. MR 464334
- 5.
- J. F. Conn, Non-abelian minimal closed ideals of transitive Lie algebras, Ph.D. thesis, Princeton Univ., Princeton, N. J., 1978. MR 595686
- 6.
- H. Goldschmidt, Existence theorems for analytic linear partial differential equations, Ann. of Math. (2) 86 (1967), 246-270. MR 219859
- 7.
- H. Goldschmidt, Prolongations of linear partial differential equations. I. A conjecture of Élie Cartan, Ann. Sci. École Norm. Sup. (4) 1 (1968), 417-444. MR 235584
- 8.
- H. Goldschmidt, On the Spencer cohomology of a Lie equation, Proc. Sympos. Pure Math., vol. 23 Amer. Math. Soc., Providence, R. I., 1973, pp. 379-385. MR 343322
- 9.
- H. Goldschmidt, Sur la structure des équations de Lie: I. Le troisième théorème fondamental, J. Differential Geometry 6 (1972), 357-373. MR 301768
- 10.
- H. Goldschmidt, Sur la structure des équations de Lie: II. Équations formellement transitives, J. Differential Geometry 7 (1972), 67-95. MR 326783
- 11.
- H. Goldschmidt, Sur la structure des équations de Lie: III. La cohomologie de Spencer, J. Differential Geometry 11 (1976), 167-223. MR 517115
- 12.
- H. Goldschmidt and D. Spencer, On the non-linear cohomology of Lie equations. I, II, Acta Math. 136 (1976), 103-239. MR 445566
- 13.
- H. Goldschmidt and D. Spencer, On the non-linear cohomology of Lie equations. III, IV, J. Differential Geometry 13 (1978).
- 14.
- V. W. Guillemin, A Jordan-Hölder decomposition for a certain class of infinite dimensional Lie algebras, J. Differential Geometry 2 (1968), 313-345. MR 263882
- 15.
- V. W. Guillemin and S. Sternberg, An algebraic model of transitive differential geometry, Bull. Amer. Math. Soc. 70 (1964), 16-47. MR 170295
- 16.
- V. W. Guillemin and S. Sternberg, The Lewy counterexample and the local equivalence problem for G-structures, J. Differential Geometry 1 (1967), 127-131. MR 222800
- 17.
- A. Kumpera and D. Spencer, Lie equations. Vol. I. General theory, Ann. of Math. Studies No. 73, Princeton Univ. Press and Univ. of Tokyo Press, 1972. MR 380908
- 18.
- M. Kuranishi and A. A. M. Rodrigues, Quotients of pseudo groups by invariant fiberings, Nagoya Math. J. 24 (1964), 109-128. MR 168705
- 19.
- B. Malgrange, Équations de Lie. I, II, J. Differential Geometry 6 (1972), 503-522; 7 (1972), 117-141. MR 326784
- 20.
- P. Molino, Théorie des G-structures: Le problème d'équivalence. Lecture Notes in Math., vol. 588, Springer-Verlag, Berlin and New York, 1977. MR 517117
- 21.
- A. S. Pollack, The integrability problem for pseudogroup structures, J. Differential Geometry 9 (1974), 355-390. MR 353383
- 22.
- D. C. Spencer, Deformation of structures on manifolds defined by transitive, continuous pseudogroups. I, II, Ann. of Math. (2) 76 (1962), 306-445. MR 156363
Similar Articles:
Retrieve articles in Bulletin of the American Mathematical Society
with MSC
(1970):
58H05, 22E65, 58G99, 35N10, 53C10
Retrieve articles in all Journals with MSC
(1970):
58H05, 22E65, 58G99, 35N10, 53C10
Additional Information:
DOI:
10.1090/S0002-9904-1978-14492-9
PII:
S 0002-9904(1978)14492-9
|