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Gauge theories on four dimensional Riemannian manifolds. (English) Zbl 0502.53022

MSC:
53C05 Connections, general theory
53C80 Applications of global differential geometry to the sciences
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[1] Atiyah, M.F., Bott, R.: On the Yang-Mills equations over Riemann surfaces (preprint) · Zbl 0509.14014
[2] Atiyah, M.F., Bott, R., Patodi, V.K.: On the heat equation and the index theorem. Invent. Math.19, 279-330 (1973) · Zbl 0257.58008 · doi:10.1007/BF01425417
[3] Atiyah, M.F., Bott, R., Shapiro, A.: Clifford modules. Topology3, Suppl. 1, 3-38 (1964)
[4] Atiyah, M.F., Hitchin, N., Singer, I.: Self-duality in four-dimensional Riemannian geometry. Proc. R. Soc. (London) A362, 425-461 (1978) · Zbl 0389.53011
[5] Atiyah, M.F., Singer, I.: The index of elliptic operators. III. Ann. Math.87, 546-604 (1968) · Zbl 0164.24301 · doi:10.2307/1970717
[6] Bourguignon, J.P., Lawson, H.B.: Stability and isolation phenomena for Yang-Mills fields. Commun. Math. Phys.79, 189-230 (1981) · Zbl 0475.53060 · doi:10.1007/BF01942061
[7] Fegan, H.: Conformally invariant first order differential operators. Q.J. Math.27, 371-378 (1976) · Zbl 0334.58016 · doi:10.1093/qmath/27.3.371
[8] Hawking, S., Ellis, G.: The large scale curvature of space-time. Cambridge University Press 1973 · Zbl 0265.53054
[9] Hitchin, N.: Harmonic spinors. Adv. Math.14, 1-55 (1974) · Zbl 0284.58016 · doi:10.1016/0001-8708(74)90021-8
[10] Hitchin, N.: Linear field equations on self-dual spaces. Proc. R. Soc. (London) A370, 173-191 (1981) · Zbl 0436.53058
[11] Kobayashi, S., Nomizu, K.: Foundations of differential geometry, Vol. I. New York: Interscience 1963 · Zbl 0119.37502
[12] Mitter, P.K., Viallet, C.M.: On the bundle of connections and the gauge orbit manifold in Yang-Mills theory. Commun. Math. Phys.79, 457-472 (1981) · Zbl 0474.58004 · doi:10.1007/BF01209307
[13] Morrey, C.B.: Multiple integrals in the calculus of variations. Berlin, Heidelberg, New York: Springer 1966 · Zbl 0142.38701
[14] Palais, R.: Foundations of global non-linear analysis. New York: Benjamin 1968 · Zbl 0164.11102
[15] Samelson, H.: Notes on Lie algebras. New York: Van Nostrand, Reinhold 1969 · Zbl 0209.06601
[16] Singer, I.M., Thorpe, J.: The curvature of 4-dimensional Einstein spaces. In: Global analysis, Papers in honor of Kodaira, K., Spencer, D.C., Iyanaga, S. (eds.). Princeton NS: Princeton University Press 1969, 1969, pp. 355-365 · Zbl 0199.25401
[17] Sternberg, S.: On the role of field theories in our physical conception of geometry. In: Differential geometrical methods in mathematical physics, Vol. II. Bleuler, Petry, Reetz (eds.). Lecture Notes in Mathematics, Vol. 1b, pp. 1-55. Berlin, Heidelberg, New York: Springer 1978
[18] Stredder, P.: Natural differential operators on riemannian manifolds and representations of the orthogonal and special orthogonal groups. J. Diff. Geol.10, 657-660 (1975) · Zbl 0318.53046
[19] Uhlenbeck, K.: Removable singularities in Yang-Mills fields. Commun. Math. Phys.83, 11-30 (1982) · Zbl 0491.58032 · doi:10.1007/BF01947068
[20] Uhlenbeck, K.: Connections withL p bounds on curvature. Commun. Math. Phys.83, 31-42 (1982) · Zbl 0499.58019 · doi:10.1007/BF01947069
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