A fundamental differential system of Riemannian geometry

• Rui Albuquerque ^[1]
  1. [1] Universidade de Évora

     Universidade de Évora

     Senhora da Saúde, Portugal

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 35, Nº 7, 2019, págs. 2221-2250
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • We discover a fundamental exterior differential system of Riemannian geometry; indeed, an intrinsic and invariant global system of differential forms of degree n associated to any given oriented Riemannian manifold M of dimension n+1. The framework is that of the tangent sphere bundle of M. We generalise to a Riemannian setting some results from the theory of hypersurfaces in flat Euclidean space. We give new applications and examples of the associated Euler–Lagrange differential systems.