Transformations of conformally invariant -models
For (M, [g]) a conformal manifold of signature (p, q) and dimension at least three, the conformal holonomy group Hol(M, [g]) ⊂ O(p + 1, q + 1) is an invariant induced by the canonical Cartan geometry of (M, [g]). We give a description of all possible connected conformal holonomy groups which act transitively on the Möbius sphere S p,q, the homogeneous model space for conformal structures of signature (p, q). The main part of this description is a list of all such groups which also act irreducibly...
Given that a connected Lie group with nilpotent radical acts transitively by isometries on a connected Riemannian manifold , the structure of the full connected isometry group of and the imbedding of in are described. In particular, if equals its derived subgroup and its Levi factors are of noncompact type, then is normal in . In the special case of a simply transitive action of on , a transitive normal subgroup of is constructed with and a sufficient condition is given...
Consider two foliations and , of dimension one and codimension one respectively, on a compact connected affine manifold . Suppose that ; and . In this paper we show that either is given by a fibration over , and then has a great degree of freedom, or the trace of is given by a few number of types of curves which are completely described. Moreover we prove that has a transverse affine structure.
We introduce an explicit procedure to generate natural operators on manifolds with almost Hermitian symmetric structures and work out several examples of this procedure in the case of almost Grassmannian structures.
In the homogeneous space Sol, a translation surface is parametrized by , where and are curves contained in coordinate planes. In this article, we study translation invariant surfaces in , which has finite type immersion.
Dans ces notes il sera expliqué que la propriété est vérifiée par le groupe de Heisenberg muni de la distance de Carnot-Carathéodory et de la mesure de Lebesgue. Cette propriété correspond pour les espaces métriques mesurés à une courbure de Ricci positive. Comme application, les mesures interpolées par transport de mesure sont absolument continues. En revanche, la courbure-dimension , une autre courbure de Ricci synthétique adaptée aux espaces métriques mesurés est fausse pour .