# The c-map on groups

## TL;DR

This paper investigates the intrinsic properties of homogeneous projective special Kähler structures on groups, providing new defining equations and demonstrating their relation to quaternionic Kähler structures via the c-map.

## Contribution

It introduces an intrinsic, computation-free definition of homogeneous projective special Kähler structures on groups and explores their connection to quaternionic Kähler structures through the c-map.

## Key findings

- Intrinsic defining equations for homogeneous projective special Kähler structures
- The c-map transforms these structures into left-invariant quaternionic Kähler structures on Lie groups
- Emphasis on integrability conditions associated with these structures

## Abstract

We study the projective special Kaehler condition on groups, providing an intrinsic definition of homogeneous projective special Kaehler that includes the previously known examples. We give intrinsic defining equations that may be used without resorting to computations in the special cone, and emphasise certain associated integrability equations. The definition is shown to have the property that the image of such structures under the c-map is necessarily a left-invariant quaternionic Kaehler structure on a Lie group.