Revista Matemática Iberoamericana


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Volume 33, Issue 2, 2017, pp. 449–468
DOI: 10.4171/RMI/944

Curvature locus and principal configurations of submanifolds of Euclidean space

Juan José Nuño Ballesteros[1], María Carmen Romero Fuster[2] and Federico Sánchez-Bringas[3]

(1) Universitat de València, Spain
(2) Universitat de València, Spain
(3) Universidad Nacional Autónoma de México, Mexico

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.

Keywords: Umbilicity, $\nu$-principal curvature foliation, curvature locus, normal curvature, convexity

Nuño Ballesteros Juan José, Romero Fuster María Carmen, Sánchez-Bringas Federico: Curvature locus and principal configurations of submanifolds of Euclidean space. Rev. Mat. Iberoamericana 33 (2017), 449-468. doi: 10.4171/RMI/944