Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 13 (2017), 086, 28 pages      arXiv:1603.07915      https://doi.org/10.3842/SIGMA.2017.086

Parallelisms & Lie Connections

David Blázquez-Sanz a and Guy Casale b
a) Universidad Nacional de Colombia, Sede Medellín, Facultad de Ciencias, Escuela de Matemáticas, Calle 59A No. 63 - 20, Medellín, Antioquia, Colombia
b) IRMAR, Université de Rennes 1, Campus de Beaulieu, bât. 22-23, 263 avenue du Général Leclerc, CS 74205, 35042 RENNES Cedex, France

Received September 16, 2016, in final form October 25, 2017; Published online November 04, 2017

Abstract
The aim of this article is to study rational parallelisms of algebraic varieties by means of the transcendence of their symmetries. The nature of this transcendence is measured by a Galois group built from the Picard-Vessiot theory of principal connections.

Key words: parallelism; isogeny; $G$-structure; linear connection; principal connection; differential Galois theory.

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