منابع مشابه
Constructing Complete Projectively Flat Connections
Theorem 1. Let T 2 be the two dimensional torus. Then for any positive integer m there is a complete torsion free projectively flat connection, ∇, on T 2 such that for any point p ∈ T 2 there is a point q ∈ T 2 with the property that any broken ∇-geodesic between p and q has at least m breaks. Moreover if T 2 is viewed as a Lie group in the usual manner, this connection is invariant under trans...
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where FA denotes the curvature of A. In four dimensions, FA decomposes into its self-dual and anti-self-dual components, FA = F + A + F − A , where F A denotes the projection onto the ±1 eigenspace of the Hodge star operator. A connection is called self-dual (respectively anti-self-dual) if FA = F + A (respectively FA = F − A ). A connection is called an instanton if it is either self-dual or a...
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Consider a Yang-Mills connection over a Riemann manifold M = M, n ≥ 3, where M may be compact or complete. Then its energy must be bounded from below by some positive constant, if M satisfies certain conditions, unless the connection is flat.
متن کاملThe Volume Measure for Flat Connections as Limit of the Yang–Mills Measure
We prove that integration over the moduli space of flat connections can be obtained as a limit of integration with respect to the Yang– Mills measure defined in terms of the heat kernel for the gauge group. In doing this we also give a rigorous proof of Witten’s formula for the symplectic volume of the moduli space of flat connections. Our proof uses an elementary identity connecting determinan...
متن کاملRemovable Singularities for Yang-mills Connections in Higher Dimensions
We prove several removable singularity theorems for singular Yang-Mills connections on bundles over Riemannian manifolds of dimensions greater than four. We obtain the local and global removability of singularities for Yang-Mills connections with L∞ or L n 2 bounds on their curvature tensors, with weaker assumptions in the L∞ case and stronger assumptions in the L n 2 case. With the global gaug...
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ژورنال
عنوان ژورنال: Kyushu Journal of Mathematics
سال: 2009
ISSN: 1340-6116,1883-2032
DOI: 10.2206/kyushujm.64.49