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Bifurcations of simple umbilical points defined by vector fields normal to a surface immersed in ℝ4

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Abstract

Thev-principal configuration of an immersed surfaceM in ℝ4 is the set formed by the umbilical points and the lines of principal curvatures with respect to a unitary smooth vector fieldv normal toM. In this article we describe the bifurcation diagram ofv-principal configurations, wherev is parametrized in the space of 1-jets of normal vector fields which define an isolated umbilical point. Versal unfoldings of the nonlocally stable simple umbilical points are obtained.

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Authors and Affiliations

  1. Departamento de Matemáticas, Facultad de Ciencias, UASLP, Zone Universitaria, 78290, San Luis Potosí, S.L.P., Mérico

    Matías Navarro

  2. Departamento de Matemáticas, Facultad de Ciencias, UNAM, Ciudad Universitaria, 04510, México, D.F., México

    Federico Sánchez-Bringas

Authors
  1. Matías Navarro
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  2. Federico Sánchez-Bringas
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Corresponding author

Correspondence to Matías Navarro.

Additional information

Submitted by E. Lacomba

Partially supported by Proyecto D.G.A.P.A. IN 127498 UNAM.

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Navarro, M., Sánchez-Bringas, F. Bifurcations of simple umbilical points defined by vector fields normal to a surface immersed in ℝ4 . Qual. Th. Dyn. Syst 2, 359–380 (2001). https://doi.org/10.1007/BF02969346

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