Stable umbilical points of a W-congruence
Abstract
The class of W-congruences is a central object of Projective Differential Geometry. Nevertheless, their singularities has not been extensively studied. In this paper we prove a characterization of W-congruences that allow us to study their umbilical points. We describe examples of isolated stable umbilical points of type Am, m∈\1,2,3,4\, and discuss some partial results concerning the generalization of these results to any m∈N\∞\.
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