Generic Reductions of an Integrable G-Structure and an Infinitesimal Version of Cartan-Sternberg Reduction
Given an integrable G-structure P and a closed subgroup H of G, we assign to each H-reduction of P a singular set in the base manifold. Our first main result is that generically, this singular set is a finite disjoint union of submanifolds (our theorem generalizes an unpublished result of L. Lipskie). The group can often be reduced even further off this singular set by a method of Cartan and Sternberg.
University of Illinois - Urbana-Champaign
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University of Illinois at Urbana-Champaign