Classification of complete projective special real surfaces

TL;DR

This paper classifies all complete projective special real surfaces and explores their implications for higher-dimensional special Kähler and quaternionic Kähler manifolds via supergravity maps.

Contribution

It provides a complete classification of these surfaces and analyzes their role in constructing special geometric structures through supergravity mappings.

Findings

All complete projective special real surfaces are classified.

They induce complete projective special Kähler manifolds of dimension 6.

These Kähler manifolds lead to complete quaternionic Kähler manifolds of dimension 16.

Abstract

We determine all complete projective special real surfaces. By the supergravity r-map, they give rise to complete projective special K\"ahler manifolds of dimension 6, which are distinguished by the image of their scalar curvature function. By the supergravity c-map, the latter manifolds define in turn complete quaternionic K\"ahler manifolds of dimension 16.