Abstract
It is proved that every immersion of a compact oriented two-dimensional smooth manifold into R3 can be arbitrarily C2-approximated by smooth immersions β whose principal configurations Pβ = (Uβ ,Fβ ,fβ) defined by umbilical points and families of lines of principal curvature, are stable under C3-sufficiently small perturbations of β. Actually, the elements β are found in the class S r, r≥4, of C3-principally structurally stable immersions, introduced in [3].
Examples of immersions with recurrent lines of principal curvature are also given.
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Gutiérrez, C., Sotomayor, J. (1983). An approximation theorem for immersions with stable configurations of lines of principal curvature. In: Palis, J. (eds) Geometric Dynamics. Lecture Notes in Mathematics, vol 1007. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061423
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DOI: https://doi.org/10.1007/BFb0061423
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