Connections with prescribed curvature and Yang-Mills currents : the semi-simple case

Dennis Deturck; Hubert Goldschmidt; Janet Talvacchia

Annales scientifiques de l'École Normale Supérieure (1991)

  • Volume: 24, Issue: 1, page 57-112
  • ISSN: 0012-9593

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Deturck, Dennis, Goldschmidt, Hubert, and Talvacchia, Janet. "Connections with prescribed curvature and Yang-Mills currents : the semi-simple case." Annales scientifiques de l'École Normale Supérieure 24.1 (1991): 57-112. <http://eudml.org/doc/82291>.

@article{Deturck1991,
author = {Deturck, Dennis, Goldschmidt, Hubert, Talvacchia, Janet},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {real-analytic solutions; connection; principal bundle; inhomogeneous Yang-Mills equation},
language = {eng},
number = {1},
pages = {57-112},
publisher = {Elsevier},
title = {Connections with prescribed curvature and Yang-Mills currents : the semi-simple case},
url = {http://eudml.org/doc/82291},
volume = {24},
year = {1991},
}

TY - JOUR
AU - Deturck, Dennis
AU - Goldschmidt, Hubert
AU - Talvacchia, Janet
TI - Connections with prescribed curvature and Yang-Mills currents : the semi-simple case
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1991
PB - Elsevier
VL - 24
IS - 1
SP - 57
EP - 112
LA - eng
KW - real-analytic solutions; connection; principal bundle; inhomogeneous Yang-Mills equation
UR - http://eudml.org/doc/82291
ER -

References

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  1. [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. Zbl0726.58002MR92h:58007
  2. [2] D. DETURCK, Existence of Metrics with Prescribed Ricci Curvature : Local Theory (Invent. Math., Vol. 65, 1981, pp. 179-207). Zbl0489.53014MR83b:53019
  3. [3] D. DETURCK and J. TALVACCHIA, Connections with Prescribed Curvature [Ann. Inst. Fourier (Grenoble), Vol. 37, fasc. 4, 1987, pp. 29-44]. Zbl0627.53027MR89d:53058
  4. [4] H. GOLDSCHMIDT, Existence Theorems for Analytic Linear Partial Differential Equations (Ann. of Math., Vol. 86, 1967, pp. 246-270). Zbl0154.35103MR36 #2933
  5. [5] H. GOLDSCHMIDT, Integrability Criteria for Systems of Non-Linear Partial Differential Equations (J. Differential Geom., Vol. 1, 1967, pp. 267-307). Zbl0159.14101MR37 #1746
  6. [6] S. KOBAYASHI and K. NOMIZU, Foundations of Differential Geometry, Vol. I, Interscience Publishers, New York, London, 1963. Zbl0119.37502MR27 #2945
  7. [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). Zbl0099.25603MR22 #5693
  8. [8] B. KOSTANT, Lie Group Representations on Polynomial Rings (Amer. J. Math., Vol. 85, 1963, pp. 327-404). Zbl0124.26802MR28 #1252
  9. [9] B. MALGRANGE, Équations de Lie. II (J. Differential Geom., Vol. 7, 1972, pp. 117-141). Zbl0264.58009MR48 #5128
  10. [10] J. TALVACCHIA, Prescribing the Curvature of a Principal-Bundle Connection (Ph. D. thesis, University of Pennsylvania, 1989). 
  11. [11] S. P. TSAREV, Which 2-forms are Locally, Curvature Forms ? (Functional Anal. Appl., Vol. 16, 1982, pp. 235-237). Zbl0516.53014MR84e:53043
  12. [12] V. S. VARADARAJAN, On the Ring of Invariant Polynomials on a Semisimple Lie Algebra (Amer. J. Math., Vol. 90, 1968, pp. 308-317). Zbl0205.33303MR37 #1529
  13. [13] V. S. VARADARAJAN, Lie Groups, Lie Algebras and their Representations, Graduate Texts in Math., Vol. 102, Springer-Verlag, New York, Berlin, Heidelberg, 1984. Zbl0955.22500MR85e:22001

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