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Memorias de investigación
Artículos en revistas:
Geometric structures associated to the Chern connection attached to a SODE
Año:2013
Áreas de investigación
  • Geometría diferencial
Datos
Descripción
To each second-order ordinary differential equation $\sigma $ on a smooth manifold $M$ a $G$-structure $P^\sigma $ on $J^1(\mathbb{R},M)$ is associated and the Chern connection $\nabla ^\sigma $ attached to $\sigma $ is proved to be reducible to $P^\sigma $; in fact, $P^\sigma $ coincides generically with the holonomy bundle of $\nabla ^\sigma $. The cases of unimodular and orthogonal holonomy are also dealt with. Two characterizations of the Chern connection are given: The first one in terms of the corresponding covariant derivative and the second one as the only principal connection on $P^\sigma $ with prescribed torsion tensor field. The properties of the curvature tensor field of $\nabla ^\sigma $ in relationship to the existence of special coordinate systems for $\sigma $ are studied. Moreover, all the odd-degree characteristic classes on $P^\sigma $ are seen to be exact and the usual characteristic classes induced by $\nabla ^\sigma $ determine the Chern classes of $M$. The maximal group of automorphisms of the projection $p\colon \mathbb{R}\times M\to \mathbb{R}$ with respect to which $\nabla ^\sigma $ has a functorial behaviour, is proved to be the group of $p$-vertical automorphisms. The notion of a differential invariant under such a group is defined and stated that second-order differential invariants factor through the curvature mapping; a structure is thus established for KCC theory.
Internacional
Si
JCR del ISI
Si
Título de la revista
Differential Geometry and its applications
ISSN
0926-2245
Factor de impacto JCR
0,65
Información de impacto
Volumen
31
DOI
Número de revista
Desde la página
437
Hasta la página
462
Mes
SIN MES
Ranking
Mathematics
Esta actividad pertenece a memorias de investigación
Participantes
  • Autor: Maria Eugenia Rosado Maria (UPM)
  • Autor: Jaime Muñoz Masqué (CSIC)
Grupos de investigación, Departamentos, Centros e Institutos de I+D+i relacionados
  • Creador: Departamento: Matemática Aplicada a la Edificación, al Medio Ambiente y al Urbanismo
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