Variedades riemannianas abertas : rigidez das fronteiras ideais e geometria das variedades com curvatura minimal radial assintoticamente não negativa

AUTOR(ES)
DATA DE PUBLICAÇÃO

2001

RESUMO

In this Thesis we present two results, basically: (1) The construction on R8, of a metric g, of nonnegative Ricci curvature Ricg ? 0, such that the open manifold (R8,g) has Ideal Boundaries of different dimensions (differing, in this sense, from the manifolds of nonnegative sectional curvature K ? O); (2) We study a class of pointed open Riemannian manifolds (MN, o,g) whose minimal radial curvature K o min ? -k(dM (o, .)), where k is a nonnegative function of quadratic decay and dM ( ,,) is the distance function on MN induced by the Riemannian metric. We have rewritten the Rauch, Bishop-Gromov and Toponogov Comparison Theorems for this class of manifolds, comparing them with manifolds M-KN, rotationally symmetric (diffeomorphic to the Euclidean space) of curvature -k(t), instead of space forros, as it is usual. As a consequence of Rauch Comparison Theorem, we have shown the existence of a metric contraction, ? : M-KN ? Mn, and then we applied such fundamental result, in the proof of a Packing Lemma, and subsequently Existence and Uniqueness Theorem for Tangent Cones at Infinity for this class of manifolds, what shows that such class must have a much more rigid structure then the class of manifolds with Ric ? O

ASSUNTO(S)

geometria diferencial variedades riemanianas curvatura

ACESSO AO ARTIGO

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