Espacios de "moduli" de "jets" de estructuras geométricas en un punto

Dirixida por:
  1. José Navarro Garmendia Director

Universidade de defensa: Universidad de Extremadura

Fecha de defensa: 19 de xaneiro de 2018

  1. Eduardo García Río Presidente
  2. Rui Albuquerque Secretario/a
  3. Pedro José Sancho de Salas Vogal

Tipo: Tese


The problem of classification, no matter what the objects to be classified may be, is a ubiquitous problem in Mathematics –specially in Differential Geometry. The aim of this thesis is to focus on the equivalence of jets of certain geometrical structures at a point. We consider this might be a first step to study the more interesting problem of local classification of those structures. To be more precise, if we denote by JₚʳF the fiber bundle of r-jets of sections of the natural bundle F→X of order s, and Difₚʳ⁺ˢ stands for the group of (r+s)-jets of local diffeomorphisms in the smooth manifold X leaving the point p fixed, our problem consists in analyzing the nature of the following quotient space: JₚʳF / Difₚʳ⁺ˢ. In particular, in this work, the bundle F is that of linear connections (in chapter 2), and that of metrics (in chapter 3). Our way to deal with the question above pays special attention to the study of differential invariants of order r associated to the geometric structures we wish to analyze; that is, “differentiable” real functions on the quotient JₚʳF / Difₚʳ⁺ˢ.