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Variétés riemanniennes isométriques à l'infini.

Thierry Coulhon, Laurent Saloff-Coste (1995)

Revista Matemática Iberoamericana

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.

Varieties of minimal rational tangents of codimension 1

Jun-Muk Hwang (2013)

Annales scientifiques de l'École Normale Supérieure

Let  X be a uniruled projective manifold and let  x be a general point. The main result of [2] says that if the ( - K X ) -degrees (i.e., the degrees with respect to the anti-canonical bundle of  X ) of all rational curves through x are at least dim X + 1 , then X is a projective space. In this paper, we study the structure of  X when the ( - K X ) -degrees of all rational curves through x are at least dim X . Our study uses the projective variety 𝒞 x T x ( X ) , called the VMRT at  x , defined as the union of tangent directions to the rational curves...

Vector fields and connection on fibred manifolds

Dekrét, Anton (1990)

Proceedings of the Winter School "Geometry and Physics"

[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.

Veech Groups of Loch Ness Monsters

Piotr Przytycki, Gabriela Schmithüsen, Ferrán Valdez (2011)

Annales de l’institut Fourier

We classify Veech groups of tame non-compact flat surfaces. In particular we prove that all countable subgroups of G L + ( 2 , R ) avoiding the set of mappings of norm less than 1 appear as Veech groups of tame non-compact flat surfaces which are Loch Ness monsters. Conversely, a Veech group of any tame flat surface is either countable, or one of three specific types.

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