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On exponential Yang-Mills connections

✍ Scribed by Fumiaki Matsura; Hajime Urakawa

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 730 KB
Volume: 17
Category: Article
ISSN: 0393-0440
DOI: 10.1016/0393-0440(94)00041-2

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✦ Synopsis

In this paper, we study a new functional, i.e., the exponential Yang-Mills functional ~'~t" e on the space of all smooth connections Vof a vector bundle E over a compact Riemannian manifold (M, g) which is defined by

where II R v 11 is the curvature tensor of a connection V. A critical point of Y/e~'e is called an exponential Yang-Mills connection. If IIR vii is constant, a smooth connection V is an exponential Yang-Mills connection if it is a Yang-Mills one. We show for any vector bundle E, that the functional y~'~ admits a minimising connection V which is C~-HOlder continuous for all 0 < a < 1. We show the existence theorem of a smooth exponential Yang-Mills connection and study its properties and the second variation formula.

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