Whitney umbrellas and swallowtails
Takashi Nishimura

TL;DR
This paper establishes a mathematical correspondence between Whitney umbrellas of pedal unfolding type and normalized swallowtails using concepts from Legendrian singularity theory, revealing a deep geometric connection.
Contribution
It introduces new notions of pedal unfolding type and normalized Legendrian map-germs, and demonstrates a natural one-to-one correspondence between Whitney umbrellas and swallowtails.
Findings
Established a correspondence between Whitney umbrellas and swallowtails.
Introduced the concepts of pedal unfolding type and normalized Legendrian map-germs.
Connected the fundamental theorem of calculus to singularity theory.
Abstract
In this paper, we introduce the notions of map-germs of pedal unfolding type and normalized Legendrian map-germs; and then we show that the fundamental theorem of calculus provides a natural one to one correspondence between Whitney umbrellas of pedal unfolding type and normalized swallowtails.
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Taxonomy
TopicsFuzzy and Soft Set Theory · Advanced Differential Equations and Dynamical Systems
