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.
Rezensionen / Stimmen
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)
Reihe
Auflage
Sprache
Verlagsort
Verlagsgruppe
Illustrationen
8
1 farbige Abbildung, 8 s/w Abbildungen
XXI, 399 p. 9 illus., 1 illus. in color.
Dateigröße
ISBN-13
978-3-0348-0534-6 (9783034805346)
DOI
10.1007/978-3-0348-0534-6
Schweitzer Klassifikation
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.
