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Non-stationary smooth geometric structures for contracting measurable cocycles
We implement a differential-geometric approach to normal forms for contracting measurable cocycles to \mbox{Diff}^q({\bf R}^n, {\bf 0}), . We obtain resonance polynomial normal forms for the contracting cocycle and its centralizer, via changes of coordinates. These are interpreted as nonstationary invariant differential-geometric structures. We also consider the case of contracted foliations in a manifold, and obtain homogeneous structures on leaves for an action of the group of subresonance polynomial diffeomorphisms together with translations
C^1 Deformations of almost-Grassmannian structures with strongly essential symmetry
We construct a family of -almost Grassmannian structures of regularity
, each admitting a one-parameter group of strongly essential
automorphisms, and each not flat on any neighborhood of the higher-order fixed
point. This shows that Theorem 1.3 of [9] does not hold assuming only
regularity of the structure (see also [2, Prop 3.5]).Comment: 24 p
Conformal actions of nilpotent groups on pseudo-Riemannian manifolds
We study conformal actions of connected nilpotent Lie groups on compact
pseudo-Riemannian manifolds. We prove that if a type-(p,q) compact manifold M
supports a conformal action of a connected nilpotent group H, then the degree
of nilpotence of H is at most 2p+1, assuming p <= q; further, if this maximal
degree is attained, then M is conformally equivalent to the universal
type-(p,q), compact, conformally flat space, up to finite covers. The proofs
make use of the canonical Cartan geometry associated to a pseudo-Riemannian
conformal structure.Comment: 41 pages, 3 figures. Article has been shortened from previous
version, and several corrections have been made according to referees'
suggestion
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