Indefinite symmetric spaces with $G_{2(2)}$-structure

TL;DR

This paper classifies all indecomposable pseudo-Riemannian symmetric spaces of signature (4,3) with holonomy contained in the exceptional Lie group $G_{2(2)}$, expanding understanding of special geometric structures.

Contribution

It provides a complete classification of such symmetric spaces, identifying all possible geometries with $G_{2(2)}$-holonomy in signature (4,3).

Findings

Classified all indecomposable symmetric spaces with $G_{2(2)}$ holonomy.

Identified the geometric structures compatible with $G_{2(2)}$ in signature (4,3).

Enhanced understanding of special holonomy in pseudo-Riemannian geometry.

Abstract

We determine all indecomposable pseudo-Riemannian symmetric spaces of signature (4,3) whose holonomy is contained in $G_{2(2)}\subset SO(4,3)$.