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arXiv · 2504.07289

Stable umbilical points of a W-congruence

Marcos Craizer·Ronaldo Alves Garcia
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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 $A_m$, $m\in\{1,2,3,4\}$, and discuss some partial results concerning the generalization of these results to any $m\in\mathbb{N}\cup\{\infty\}$.

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Marcos Craizer, Ronaldo Alves Garcia. 2025-04-09. Stable umbilical points of a W-congruence. https://arxiv.org/abs/2504.07289

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