Equiaffine structure on frontals

TL;DR

This paper extends equiaffine geometry to frontals, defining a Blaschke vector field, establishing conditions for its existence, and proving a fundamental theorem analogous to classical affine differential geometry.

Contribution

It introduces the concept of a Blaschke vector field for frontals and establishes a fundamental theorem for this new setting, broadening affine differential geometry.

Findings

Defined the Blaschke vector field for frontals

Established necessary and sufficient conditions for its existence

Presented a fundamental theorem for frontals in affine geometry

Abstract

In this paper, we generalize the idea of equiaffine structure to the case of frontals and we define the Blaschke vector field of a frontal. We also investigate some necessary and sufficient conditions that a frontal needs to satisfy to have a Blaschke vector field and provide some examples. Finally, taking the theory developed here into account we present a fundamental theorem, which is a version for frontals of the fundamental theorem of affine differential geometry.