Abstract
The last five decades have witnessed many developments in the theory of harmonic maps. To become acquainted to some of these, the reader is referred to two reports and a survey paper by Eells and Lemaire [119, 122, 124] about the developments of harmonic maps up to 1988 for details. Several books on harmonic maps [203, 205, 206, 389, 425] are also available. In this chapter, we follow the notions and notations of harmonic maps between Riemannian manifolds by Eells- Sampson [129] in the introduction.We discuss the crucial topics in harmonic maps including fundamentals, regularity, maps of surfaces, maps of KRahler manifolds, maps into groups and Grassmannians, harmonic maps, loop groups, and integrable systems, harmonicmorphisms, maps of singular spaces, and transversally harmonic maps. Since the theory of harmonic maps has been developed over half a century, it is impossible to provide full details. However, we try to present the most important components of the topics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Bibliography
R. Ababou, P. Baird, J. Brossard, Polynômes semi-conformes et morphismes harmoniques. Math. Z. 231(3), 589–604 (1999)
J.-P. Bourguignon, H.B. Lawson, Stability and isolation phenomena for Yang-Mills fields. Commun. Math. Phys. 79(2), 189–230 (1981)
J. Eells, M.J. Ferreira, On representing homotopy classes by harmonic maps. Bull. Lond. Math. Soc. 23(2), 160–162 (1991)
M.C. Hong, On the conformal equivalence of harmonic maps and exponential harmonic maps. Bull. Lond. Math. Soc. 24(5), 488–492 (1992)
U. Katagiri, On the existence of Yang-Mills connections by conformal changes in higher dimensions. J. Math. Soc. Jpn. 46(1), 139–145 (1994)
F. Matsuura, H. Urakawa, On exponential Yang-Mills connections. J. Geom. Phys. 17(1), 73–89 (1995)
J. Råde, On the Yang-Mills heat equation in two and three dimensions. J. Reine Angew. Math. 431, 123–163 (1992)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Basel
About this chapter
Cite this chapter
Chiang, YJ. (2013). Exponential Yang-Mills Connections. In: Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields. Frontiers in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0534-6_9
Download citation
DOI: https://doi.org/10.1007/978-3-0348-0534-6_9
Published:
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0533-9
Online ISBN: 978-3-0348-0534-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)