Focal surfaces of wave fronts in the Euclidean 3-space
Keisuke Teramoto
TL;DR
This paper characterizes the singularities of focal surfaces of wave fronts in Euclidean 3-space using differential geometry and explores their relationship with the initial wave fronts' invariants.
Contribution
It provides a new characterization of focal surface singularities and links their geometric properties to those of the original wave fronts.
Findings
Singularities of focal surfaces are characterized by differential geometric properties.
Relationships between focal surface geometry and initial wave front invariants are established.
The study enhances understanding of wave front and focal surface geometry in Euclidean 3-space.
Abstract
We characterize singularities of focal surfaces of wave fronts in terms of differential geometric properties of the initial wave fronts. Moreover, we study relationships between geometric properties of focal surfaces and geometric invariants of the initial wave fronts.
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