The goal here is Theorem 10.1 below, which is the modification of Theorem 9.1 in the presence of an automorphism γ. The only contributions to the asymptotic expansion come from neighborhoods of fixed points in M of γ, which in the principal G-bundle P correspond to fixed points modulo the action of G. The extra ingredient needed here is the asymptotic estimate in Lemma 10.1 of the geodesic distance between two points in P which are close to the same G-orbit.
KeywordsAsymptotic Expansion Geodesic Distance Planar Rotation Hermitian Structure Riemannian Structure
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