This analysis reveals geometric properties of caustics and singularities in pseudo-spherical surfaces, indicating complexities of cuspidal forms.
We deal with pseudo-spherical surfaces admitting certain singularities and their caustics. In particular, we give characterizations of cuspidal butterfly, cuspidal lip and cuspidal beak singularities on a pseudo-spherical surface. Moreover, characterizations of certain singularities on the caustics of a pseudo-spherical surface are given. Furthermore, when the caustic has a cuspidal edge singularity, we investigate geometric invariants defined at that point.
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Keisuke Teramoto (2025) studied this question.
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