Dans cet article, nous nous intéresserons à certaines propriétés des variétés riemanniennes non compactes qui ne dépendant que de leur géométrie à l'infini; pour cela, nous utiliserons un procédé de discrétisation qui associe un graph (pondéré) à une variété.
[For the entire collection see Zbl 0699.00032.] In a previous paper [Cas. Pestovani Mat. 115, No.4, 360-367 (1990)] the author determined the set of the vector fields on TM by which connections on TM can be constructed. In this paper, he generalizes some of such constructions to the case of vector fields on fibred manifolds, giving several examples.
An explicit basis of the space of global vector fields on the Sato Grassmannian is computed and the vanishing of the first cohomology group of the sheaf of derivations is shown.
A brief exposition of Lie algebroids, followed by a discussion of vector forms and their brackets in this context - and a formula for these brackets in “deformed” Lie algebroids.
Let be the interior of a compact manifold of dimension with boundary , and be a conformally compact metric on , namely extends continuously (or with some degree of smoothness) as a metric to , where denotes a defining function for , i.e. on and , on . The restrction of to rescales upon changing , so defines invariantly a conformal class of metrics on , which is called the conformal infinity of . In the present paper, the author considers conformally compact metrics...
We give criteria of finite determinacy for the volume and multiplicities. Given an analytic set described by {v = 0}, we prove that the log-analytic expansion of the volume of the intersection of the set and a "little ball" is determined by that of the set defined by the Taylor expansion of v up to a certain order if the mapping v has an isolated singularity at the origin. We also compare the cardinalities of finite fibers of projections restricted to such a set.
We consider the distance to compact submanifolds and study volume comparison for tubular neighborhoods of compact submanifolds. As applications, we obtain a lower bound for the length of a closed geodesic of a compact Finsler manifold. When the Finsler metric is reversible, we also provide a lower bound of the injectivity radius. Our results are Finsler versions of Heintze-Karcher's and Cheeger's results for Riemannian manifolds.