Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields, 1st Edition

  • Published By:
  • ISBN-10: 3034805349
  • ISBN-13: 9783034805346
  • DDC: 516.362
  • Grade Level Range: College Freshman - College Senior
  • 399 Pages | eBook
  • Original Copyright 2013 | Published/Released June 2014
  • This publication's content originally published in print form: 2013

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Harmonic maps between Riemannian manifolds were first established by James Eells and Joseph H. Sampson 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 by Guoying Jiang 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 by the author in 2009, and bi-Yang-Mills fields (generalizing Yang-Mills fields) first investigated by Toshiyuki Ichiyama, Jun-Ichi Inoguchi and Hajime Urakawa in 2008. Other topics discussed are exponential harmonic maps, exponential wave maps and exponential Yang-Mills fields.

Table of Contents

Front Cover.
Other Frontmatter.
Title Page.
Copyright Page.
1: Harmonic Maps.
2: Wave Maps.
3: Yang-Mills Fields.
4: Biharmonic Maps.
5: Biwave Maps.
6: Bi-Yang-Mills Fields.
7: Exponentially Harmonic Maps.
8: Exponential Wave Maps.
9: Exponential Yang-Mills Connections.