Equiaffine structure on frontals

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.