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Birkhäuser - Birkhäuser Mathematics | Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields

Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields

Chiang, Yuan

2013, XXI, 399 p. 9 illus., 1 illus. in color.

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  • Presents the recent crucial developments of harmonic maps into biharmonic maps, of wave maps into biwave maps and of Yang-Mills fields into bi-Yang-Mills fields
  • Discusses exponential harmonic maps, exponential wave maps and exponential Yang-Mills fields
  • Introduces biwave maps (generalizing wave maps) and bi-Yang-Mills fields (generalizing Yang-Mills fields)
Harmonic maps between Riemannian manifolds were first established in 1964. Wave maps are harmonic maps on Minkowski spaces and have been studied since the 1990s. Yang-Mills fields, the critical points of Yang-Mills functionals of connections whose curvature tensors are harmonic, were explored by a few physicists in the 1950s, and biharmonic maps (generalizing harmonic maps) were introduced in 1986. The book presents an overview of the important developments made in these fields since they first came up. Furthermore, it introduces biwave maps (generalizing wave maps) which were first studied in 2009, and bi-Yang-Mills fields (generalizing Yang-Mills fields) first investigated in 2008. Other topics discussed are exponential harmonic maps, exponential wave maps and exponential Yang-Mills fields.

Content Level » Research

Keywords » Yang-Mills fields - bi-Yang-Mills fields - biharmonic maps - biwave maps - harmonic maps - wave maps

Related subjects » Birkhäuser Mathematics

Table of contents 

Preface. 1 Harmonic Maps.- 2 Wave Maps.-3 Yang-Mills Fields.- 4 Biharmonic Maps.- 5 Biwave Maps.- 6 Bi-Yang-Mills Fields.-7 Exponential Harmonic Maps.-8 Exponential Wave Maps.- 9. Exponential Yang-Mills Connections.- Index.​  

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