Connections with prescribed curvature and Yang-Mills currents : the semi-simple case
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 24 (1991) no. 1, p. 57-112
@article{ASENS_1991_4_24_1_57_0,
     author = {DeTurck, Dennis and Goldschmidt, Hubert and Talvacchia, Janet},
     title = {Connections with prescribed curvature and Yang-Mills currents : the semi-simple case},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Elsevier},
     volume = {Ser. 4, 24},
     number = {1},
     year = {1991},
     pages = {57-112},
     doi = {10.24033/asens.1620},
     zbl = {0722.53021},
     mrnumber = {1088271},
     language = {en},
     url = {http://www.numdam.org/item/ASENS_1991_4_24_1_57_0}
}
Deturck, Dennis; Goldschmidt, Hubert; Talvacchia, Janet. Connections with prescribed curvature and Yang-Mills currents : the semi-simple case. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 24 (1991) no. 1, pp. 57-112. doi : 10.24033/asens.1620. http://www.numdam.org/item/ASENS_1991_4_24_1_57_0/

[1] R. Bryant, S. S. Chern, R. Gardner, H. Goldschmidt and P. Griffiths, Exterior Differential Systems, Math. Sci. Res. Inst. Publ., Vol. 18, Springer-Verlag, New York, Berlin, Heidelberg, 1991. | MR 92h:58007 | Zbl 0726.58002

[2] D. Deturck, Existence of Metrics with Prescribed Ricci Curvature : Local Theory (Invent. Math., Vol. 65, 1981, pp. 179-207). | MR 83b:53019 | Zbl 0489.53014

[3] D. Deturck and J. Talvacchia, Connections with Prescribed Curvature [Ann. Inst. Fourier (Grenoble), Vol. 37, fasc. 4, 1987, pp. 29-44]. | Numdam | MR 89d:53058 | Zbl 0627.53027

[4] H. Goldschmidt, Existence Theorems for Analytic Linear Partial Differential Equations (Ann. of Math., Vol. 86, 1967, pp. 246-270). | MR 36 #2933 | Zbl 0154.35103

[5] H. Goldschmidt, Integrability Criteria for Systems of Non-Linear Partial Differential Equations (J. Differential Geom., Vol. 1, 1967, pp. 267-307). | MR 37 #1746 | Zbl 0159.14101

[6] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. I, Interscience Publishers, New York, London, 1963. | MR 27 #2945 | Zbl 0119.37502

[7] B. Kostant, The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group (Amer. J. Math., Vol. 81, 1959, pp. 973-1032). | MR 22 #5693 | Zbl 0099.25603

[8] B. Kostant, Lie Group Representations on Polynomial Rings (Amer. J. Math., Vol. 85, 1963, pp. 327-404). | MR 28 #1252 | Zbl 0124.26802

[9] B. Malgrange, Équations de Lie. II (J. Differential Geom., Vol. 7, 1972, pp. 117-141). | MR 48 #5128 | Zbl 0264.58009

[10] J. Talvacchia, Prescribing the Curvature of a Principal-Bundle Connection (Ph. D. thesis, University of Pennsylvania, 1989).

[11] S. P. Tsarev, Which 2-forms are Locally, Curvature Forms ? (Functional Anal. Appl., Vol. 16, 1982, pp. 235-237). | MR 84e:53043 | Zbl 0516.53014

[12] V. S. Varadarajan, On the Ring of Invariant Polynomials on a Semisimple Lie Algebra (Amer. J. Math., Vol. 90, 1968, pp. 308-317). | MR 37 #1529 | Zbl 0205.33303

[13] V. S. Varadarajan, Lie Groups, Lie Algebras and their Representations, Graduate Texts in Math., Vol. 102, Springer-Verlag, New York, Berlin, Heidelberg, 1984. | MR 85e:22001 | Zbl 0955.22500