Zusammenfassung
Diese Arbeit ist aus Vorträgen des Autors in einem gemeinsamen Seminar zwischen Physikern und Mathematikern an der Universität Kaiserslautern hervorgegangen. Ihr erster Teil besteht aus einem Überblick über die Differentialgeometrie der Yang-Mills Gleichungen sowie einem Beweis des Satzes von Atiyah-Ward, [4], über die Korrespondenz zwischen selbstdualen euklidischen SU(2)-Yang-Mills Feldern und gewissen holomorphen Vektorbündeln über ℙ3(ℂ).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Literatur
Atiyah, M. F. — Vorträge in Bonn, Oxford.
Atiyah, M. F., Hitchin, N. J., Singer, I. M. — Selfduality in four-dimensional Riemannian geometry. To appear in Proc. Roy. Soc.
Atiyah, M. F., Hitchin, N. J., Drinfeld, V. G., Manin, Y. I. — Construction of Instantons, Phys. Letters, 65 A, 185–187 (1978).
Atiyah, M. F., Ward, R. S. — Instantons and Algebraic Geometry, Commun. Math. Phys. 55, 117–124 (1977).
Barth, W. — Moduli of vector bundles on the projective plane, Invent. — math. 42, 63–91 (1977).
Barth, W. — Some properties of stable rank-2 vector bundles on ℙn, Math. Ann. 226, 125–150 (1977).
Barth, W., Hulek, K. — Monads and moduli of vector bundles, manuscripta math. 25, 323–347 (1978).
Douady, A. — Vorträge in Nizza, Kaiserslautern.
Grauert, H., Mülich, G. — Vektorbündel vom Rang 2 über dem n-dimensionalen komplex-projektiven Raum, manuscripta math. 16, 75–100 (1975).
Hartshorne, R. — Stable vector bundles of rank-2 on ℙ3, Math. Ann. 238, 229–280 (1978).
Hartshorne, R. — Stable vector bundles and Instantons, Commun, math. Phys. 59, 1–15 (1978).
Hirzebruch, F. — Topological methods in algebraic geometry, Springer 1966.
Horrocks, G. — Examples of rank three vector bundles on five-dimensional projective space, J. London Math. Soc. (2), 18, 15–27 (1978).
Kobayashi, S., Nomizu, K. — Foundations of differential geometry, I, II, Interscience 1963/69.
Kohn, J. J., Nirenberg, L. — On the algebra of pseudodif-ferential operators, Comm. Pure Appl. Math. 18, 269–305.(1965)
Maruyama, M. — Moduli of stable sheaves I and II, Journ. Math. Kyoto Univ., 17, 91–126 (1977) and.
Maruyama, M. — Moduli of stable sheaves I and II, Journ. Math. Kyoto Univ., 8, 557–614 (1978).
Milnor, J. W., Stasheff, J. D. — Characteristic classes, Princeton University Press 1974.
Newlander, A., Nirenberg L. — Complex coordinates in almost complex manifolds, Ann. Math. 65, 391–404 (1957).
Rawnsley, J. H. — Self-dual Yang-Mills fields, Manuskript.
Schneider, M. — Holomorphic vector bundles on ℙn, Sem. Bourbaki, n° 530, 1978/79.
Steenrod, N. — The topology of fibre bundles, Princeton 1951.
Trautmann, G. — Moduli for vector bundles on ℙn(ℂ), Math. Ann. 237, 167–186 (1978).
Trautmann, G. — Moduli von Vektorbündeln auf ℙ und Para-metrisierung von Maruyama-Schemata, in Vorbereitung.
Wells, R. O. — Differential analysis on complex manifolds, Prentice-Hall 1973.
Uhlenbeck, K. K. — Removable singularities in Yang-Mills fields, Bull. Amer. Math. Soc. (new series) 1, 579–581 (1979).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1980 Birkhäuser, Boston
About this chapter
Cite this chapter
Trautmann, G. (1980). Zur Berechnung von Yang-Mills Potentialen durch holomorphe Vektorbündel. In: Hirschowitz, A. (eds) Vector Bundles and Differential Equations. Progress in Mathematics, vol 7. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-9415-0_8
Download citation
DOI: https://doi.org/10.1007/978-1-4684-9415-0_8
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-3022-5
Online ISBN: 978-1-4684-9415-0
eBook Packages: Springer Book Archive