Dualities of differential geometric invariants on cuspidal edges on flat fronts in the hyperbolic space and the de Sitter space

TL;DR

This paper computes and compares differential geometric invariants of cuspidal edges on flat surfaces in hyperbolic and de Sitter spaces, revealing several dualities among these invariants.

Contribution

It introduces new dualities of invariants for cuspidal edges on flat surfaces in hyperbolic and de Sitter spaces, expanding understanding of their geometric properties.

Findings

Identification of dualities among invariants

Explicit computation of invariants for cuspidal edges

Insights into geometric structures in hyperbolic and de Sitter spaces

Abstract

We compute the differential geometric invariants of cuspidal edges on flat surfaces in hyperbolic $3$-space and in de Sitter space. Several dualities of invariants are pointed out.