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On the existence of a universal germ of deformations for elliptic pseudogroup structures on compact manifolds. (English) Zbl 0308.58014
MSC:
58H05 Pseudogroups and differentiable groupoids
58J10 Differential complexes
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[1] M. F. Atiyah, Complex analytic connections in fibre bundles, Trans. Amer. Math. Soc. 85 (1957), 181 – 207. · Zbl 0078.16002
[2] Avron Douglis and Louis Nirenberg, Interior estimates for elliptic systems of partial differential equations, Comm. Pure Appl. Math. 8 (1955), 503 – 538. · Zbl 0066.08002
[3] Hubert Goldschmidt, Existence theorems for analytic linear partial differential equations, Ann. of Math. (2) 86 (1967), 246 – 270. · Zbl 0154.35103
[4] Hubert Goldschmidt, Sur la structure des équations de Lie. II. Équations formellement transitives, J. Differential Geometry 7 (1972), 67 – 95 (French). · Zbl 0273.58015
[5] Victor Guillemin and Shlomo Sternberg, Deformation theory of pseudogroup structures, Mem. Amer. Math. Soc. No. 64 (1966), 80. · Zbl 0169.53001
[6] C. J. Henrich, Derivations on an arbitrary vector bundle, Trans. Amer. Math. Soc. 109 (1963), 411 – 419. · Zbl 0116.39103
[7] K. Kodaira and D. C. Spencer, On deformations of complex analytic structures. I, II, Ann. of Math. (2) 67 (1958), 328 – 466. · Zbl 0128.16901
[8] K. Kodaira and D. C. Spencer, On deformations of complex analytic structures. III. Stability theorems for complex structures, Ann. of Math. (2) 71 (1960), 43 – 76. · Zbl 0128.16902
[9] K. Kodaira, L. Nirenberg, and D. C. Spencer, On the existence of deformations of complex analytic structures, Ann. of Math. (2) 68 (1958), 450 – 459. · Zbl 0088.38004
[10] K. Kodaira and D. C. Spencer, Multifoliate structures, Ann. of Math. (2) 74 (1961), 52 – 100. · Zbl 0123.16401
[11] A. Kumpera and D. C. Spencer, Lie equations. I: General theory, Ann. of Math. Studies, vol. 73, Princeton Univ. Press, Princeton, N. J., 1972. · Zbl 0258.58015
[12] M. Kuranishi, New proof for the existence of locally complete families of complex structures, Proc. Conf. Complex Analysis (Minneapolis, 1964) Springer, Berlin, 1965, pp. 142 – 154.
[13] Masatake Kuranishi, Deformations of compact complex manifolds, Les Presses de l’Université de Montréal, Montreal, Que., 1971. Séminaire de Mathématiques Supérieures, No. 39 (Été 1969). · Zbl 0256.32014
[14] Masatake Kuranishi, A note on families of complex structures, Global Analysis (Papers in Honor of K. Kodaira), Univ. Tokyo Press, Tokyo, 1969, pp. 309 – 313.
[15] Bernard Malgrange, Equations de Lie. II, J. Differential Geometry 7 (1972), 117 – 141 (French). · Zbl 0264.58009
[16] H. K. Nickerson, On differential operators and connections, Trans. Amer. Math. Soc. 99 (1961), 509 – 539. · Zbl 0107.39503
[17] Ngô van Quê, Nonabelian Spencer cohomology and deformation theory, J. Differential Geometry 3 (1969), 165 – 211. · Zbl 0206.50403
[18] D. G. Quillen, Formal properties of overdetermined systems of linear partial differential equations, Thesis, Harvard University, 1964. · Zbl 1295.35005
[19] I. M. Singer and Shlomo Sternberg, The infinite groups of Lie and Cartan. I. The transitive groups, J. Analyse Math. 15 (1965), 1 – 114. · Zbl 0277.58008
[20] D. C. Spencer, Deformation of structures on manifolds defined by transitive, continuous pseudogroups. I. Infinitesimal deformations of structure, Ann. of Math. (2) 76 (1962), 306 – 398. , https://doi.org/10.2307/1970277 D. C. Spencer, Deformation of structures on manifolds defined by transitive, continuous pseudogroups. II. Deformations of structure, Ann. of Math. (2) 76 (1962), 399 – 445. · Zbl 0124.38601
[21] D. C. Spencer, Deformation of structures on manifolds defined by transitive, continuous pseudogroups. III. Structures defined by elliptic pseudogroups, Ann. of Math. (2) 81 (1965), 389 – 450. · Zbl 0192.29603
[22] D. C. Spencer, On deformation of pseudogroup structures, Global Analysis (Papers in Honor of K. Kodaira), Univ. Tokyo Press, Tokyo, 1969, pp. 367 – 395. · Zbl 0191.54201
[23] D. C. Spencer, Overdetermined systems of linear partial differential equations, Bull. Amer. Math. Soc. 75 (1969), 179 – 239. · Zbl 0185.33801
[24] Shlomo Sternberg, Lectures on differential geometry, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. · Zbl 0129.13102
[25] William J. Sweeney, The \?-Neumann problem, Acta Math. 120 (1968), 223 – 277. · Zbl 0159.38402
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