Yang-Mills Connections on Orientable and Nonorientable Surfaces
Yang-Mills Connections on Orientable and Nonorientable Surfaces

Author: Nan-Kuo Ho

Publisher: American Mathematical Soc.

Published: 2009-10-08

Total Pages: 113

ISBN-13: 0821844911

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In ``The Yang-Mills equations over Riemann surfaces'', Atiyah and Bott studied Yang-Mills functional over a Riemann surface from the point of view of Morse theory. In ``Yang-Mills Connections on Nonorientable Surfaces'', the authors study Yang-Mills functional on the space of connections on a principal $G_{\mathbb{R}}$-bundle over a closed, connected, nonorientable surface, where $G_{\mathbb{R}}$ is any compact connected Lie group. In this monograph, the authors generalize the discussion in ``The Yang-Mills equations over Riemann surfaces'' and ``Yang-Mills Connections on Nonorientable Surfaces''. They obtain explicit descriptions of equivariant Morse stratification of Yang-Mills functional on orientable and nonorientable surfaces for non-unitary classical groups $SO(n)$ and $Sp(n)$.

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

Author: Yuan-Jen Chiang

Publisher: Springer Science & Business Media

Published: 2013-06-18

Total Pages: 418

ISBN-13: 3034805349

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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.