Focal Surfaces of Wave Fronts in the 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.2010 Mathematics Subject Classification. 57R45, 53A05, 53A55.

Singularities of Gauss maps of wave fronts with non-degenerate singular points

“…We note that the condition 4κ t (p) 2 + κ s (p)κ c (p) 2 = 0 implies that p is not a subparabolic point of f (see [41]). Proposition 3.6.…”

On Gaussian curvatures and singularities of Gauss maps of cuspidal edges

“…For other geometric properties of these invariants, see [9,11,12,17,19,21,29,[34][35][36] for example.…”

Behavior of principal curvatures of frontals near non-front singular points and their application

“…[16]). Moreover, this quantity relates to the value of the Gaussian curvature of a focal surfaces with respect to unbounded principal curvature ( [28]). 4.2.…”