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}), $q \geq2$. We obtain resonance polynomial normal forms for the contracting cocycle and its centralizer, via $C^q$ 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 $C^q$ homogeneous structures on leaves for an action of the group of subresonance polynomial diffeomorphisms together with translations

Quasihomogeneous three-dimensional real analytic Lorentz metrics do not exist

We show that a germ of a real analytic Lorentz metric on ${\bf R}^3$ which is locally homogeneous on an open set containing the origin in its closure is necessarily locally homogeneous. We classifiy Lie algebras that can act quasihomogeneously---meaning they act transitively on an open set admitting the origin in its closure, but not at the origin---and isometrically for such a metric. In the case that the isotropy at the origin of a quasihomogeneous action is semisimple, we provide a complete set of normal forms of the metric and the action.Comment: 23 pp. Took the place of "Quasihomogeneous three-dimensional real analytic Lorentz metrics" (arXiv:1401.6272), which was withdrawn by the first author. Revised version incorporates several minor corrections, including those suggested by the refere

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

C^1 Deformations of almost-Grassmannian structures with strongly essential symmetry

We construct a family of $(2,n)$-almost Grassmannian structures of regularity $C^1$, 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 $C^1$ regularity of the structure (see also [2, Prop 3.5]).Comment: 24 p

Essential Killing fields of parabolic geometries

We study vector fields generating a local flow by automorphisms of a parabolic geometry with higher order fixed points. We develop general tools extending the techniques of [1], [2], and [3]. We apply these tools to almost Grassmannian, almost quaternionic, and contact parabolic geometries, including CR structures, to obtain descriptions of the possible dynamics of such flows near the fixed point and strong restrictions on the curvature. In some cases, we can show vanishing of the curvature on a nonempty open set. Deriving consequences for a specific geometry entails evaluating purely algebraic and representation-theoretic criteria in the model homogeneous space. Published in Indiana University Mathematics Journal.Comment: 50 pages. Minor corrections, references update

Strongly essential flows on irreducible parabolic geometries

We study the local geometry of irreducible parabolic geometries admitting strongly essential flows; these are flows by local automorphisms with higher-order fixed points. We prove several new rigidity results, and recover some old ones for projective and conformal structures, which show that in many cases the existence of a strongly essential flow implies local flatness of the geometry on an open set having the fixed point in its closure. For almost c-projective and almost quaternionic structures we can moreover show flatness of the geometry on a neighborhood of the fixed point.Comment: 34 pages. Proof of Proposition 3.1 significantly shortened, under slightly less general hypotheses (see Remark 3.1). Typos corrected and references updated. To appear in Transactions of the AM

AGB populations in post-starburst galaxies

In a previous paper we compared the SEDs of a sample of 808 K+A galaxies from the FUV to the MIR to the predictions of the spectrum synthesis models explicitly using AGB components. Here we use the new AGB-light models from C. Maraston (including less fuel for the later stages of stellar evolution and improved calibrations) to address the discrepancies between our observations and the AGB-heavy models used in our previous paper, which over-predict the infrared fluxes of post-starburst galaxies by an order of magnitude. The new models yield a much better fit to the data, especially in the near-IR, compared to previous realizations where AGB stars caused a large excess in the H and K bands. We { also compare the predictions of the M2013 models to those with BC03 and find that both reproduce the observations equally well. } We still find a significant discrepancy with { both sets of models} in the Y and J bands, which however is probably due to the spectral features of AGB stars. We also find that { both the M2013 and the BC03 models} still over-predict the observed fluxes in the UV bands, even invoking extinction laws that are stronger in these bands. While there may be some simple explanations for this discrepancy, we find that further progress requires new observations and better modelling. Excess mid-infrared emission longward of 5$\mu$m is well modelled by a $T_{dust}=300^oK$ Black-Body, which may arise from dust emission from the circumstellar envelopes of Oxygen rich M stars (expected for a metal-rich population of AGB stars).Comment: A&A accepte