Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields (Frontiers in Mathematics Book 0)

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. 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 -- Front Matter....Pages i-xxi Harmonic Maps....Pages 1-83 Wave Maps....Pages 85-162 Yang-Mills Fields....Pages 163-242 Biharmonic Maps....Pages 243-304 Biwave Maps....Pages 305-338 Bi-Yang-Mills Fields....Pages 339-350 Exponentially Harmonic Maps....Pages 351-357 Exponential Wave Maps....Pages 359-370 Exponential Yang-Mills Connections....Pages 371-378 Back Matter....Pages 379-399 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. This book 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