Semi-Riemannian structures for symmetric Galilean spacetimes

• Daniel de la Fuente ^[1] ; José A. S. Pelegrín ^[2] ; Rafael M. Rubio ^[2]
  1. [1] Universidad de Oviedo

     Universidad de Oviedo

     Oviedo, España

     
  2. [2] Universidad de Córdoba

     Universidad de Córdoba

     Cordoba, España

     
• Localización: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas ( RACSAM ), ISSN-e 1578-7303, Vol. 118, Nº. 4, 2024
• Idioma: inglés
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• Resumen

  • We introduce semi-Riemannian structures well-adapted to certain fields of observers in a Galilean spacetime. The Levi-Civita connection of such a semi-Riemannian metric will allow us to obtain variational characterizations of the Galilean geodesics as well as global results on the topological and differentiable structure of the spacetime. Moreover, these new semiRiemannian metrics provide a new way to compare the studied Newton–Cartan models with their relativistic counterparts.