Abstract

In this paper, we present an intrinsic characterisation of projective special Kähler manifolds in terms of a symmetric tensor satisfying certain differential and algebraic conditions. We show that this tensor vanishes precisely when the structure is locally isomorphic to a standard projective special Kähler structure on \/\mathrm {S}\mathrm {U})\). We use this characterisation to classify 4-dimensional projective special Kähler Lie groups.