August 5, 2025Open Access

Height functions on a cuspidal edge with a distinguished singular curve

Key Points

MAIN FINDING: The classification of submersions on a cuspidal edge shows distinct behaviors with singular curves.
KEY EVIDENCE: Contact measurements with planes are linked to the singularities of height functions on these geometric objects.
APPROACH: The study uses discriminants of versal deformations to analyze how the pairs (M,S) interact with planes.
SIGNIFICANCE: Understanding these classifications advances knowledge in differential geometry and singularity theory.

Abstract

We classify submersions on a cuspidal edge M in R^3 with a distinguished singular curve S in it. We use this classification to study the contact of the pair (M, S) with planes, which is measured by the singularities of the height functions on (M, S). The discriminants of the versal deformations of the submersions obtained are also described.

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Cite This Study

Alharbi et al. (Wed,) studied this question.

synapsesocial.com/papers/689522189f4f1c896c429cae https://doi.org/https://doi.org/10.4171/pm/2149

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