# Construction of projective special K\"ahler manifolds

## TL;DR

This paper provides an intrinsic characterization of projective special K"ahler manifolds using a symmetric tensor, leading to classification results for 4-dimensional cases and linking the structure to standard models.

## Contribution

It introduces a new intrinsic tensor-based characterization of projective special K"ahler manifolds and applies it to classify 4-dimensional Lie group examples.

## Key findings

- Tensor vanishes for standard models
- Classification of 4D projective special K"ahler Lie groups
- Characterization links to symmetric tensor conditions

## Abstract

In this paper we present an intrinsic characterisation of projective special K\"ahler 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 K\"ahler structure on $\mathrm{SU}(n,1)/\mathrm{S}(\mathrm{U}(n)\mathrm{U}(1))$. We use this characterisation to classify 4-dimensional projective special K\"ahler Lie groups.