Curvature locus and principal configurations of submanifolds of Euclidean space

• Juan José Nuño Ballesteros ^[1] ; María Carmen Romero Fuster ^[1] ; Federico Sánchez-Bringas ^[2]
  1. [1] Universitat de València

     Universitat de València

     Valencia, España

     
  2. [2] Universidad Nacional Autónoma de México

     Universidad Nacional Autónoma de México

     México

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 33, Nº 2, 2017, págs. 449-468
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • We study relations between the properties of the curvature loci of a submanifold M in Euclidean space and the behaviour of the principal configurations of M, in particular the existence of umbilic and quasiumbilic fields. We pay special attention to the case of submanifolds with vanishing normal curvature. We also characterize local convexity in terms of the curvature locus position in the normal space.