Frontiers in Mathematics

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

Authors: Chiang, Yuan

  • 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)
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  • ISBN 978-3-0348-0534-6
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  • ISBN 978-3-0348-0533-9
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About this book

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.

Reviews

From the book reviews:

“The monograph under review gathers developments in the theory of harmonic maps, wave maps, and Yang-Mills fields, and their generalisations to biharmonic maps, biwave maps, and bi-Yang-Mills fields. … The present book is a very useful text for experts in the field of harmonic and biharmonic maps, providing us with a rich and updated source of information on the subject.” (Monica Alice Aprodu, Mathematical Reviews, July, 2014)

Table of contents (9 chapters)

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-3-0348-0534-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.95
price for USA
  • ISBN 978-3-0348-0533-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields
Authors
Series Title
Frontiers in Mathematics
Copyright
2013
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
eBook ISBN
978-3-0348-0534-6
DOI
10.1007/978-3-0348-0534-6
Softcover ISBN
978-3-0348-0533-9
Series ISSN
1660-8046
Edition Number
1
Number of Pages
XXI, 399
Number of Illustrations and Tables
8 b/w illustrations, 1 illustrations in colour
Topics