# The Differential Geometry of the Orbit Space of Extended Affine Jacobi Group $A_1$

## TL;DR

This paper explores the geometric structure of the orbit space of extended affine Jacobi groups of type A1, establishing invariant theory results and constructing a Frobenius structure to deepen understanding of their symmetry properties.

## Contribution

It introduces extensions of Jacobi groups of A1, proves an invariant theory analogue of Chevalley's theorem, and constructs a Frobenius structure on the orbit space.

## Key findings

- Proved an analogue of Chevalley's theorem for extended Jacobi groups.
- Constructed a Dubrovin-Frobenius structure on the orbit space.
- Established foundational geometric properties of the orbit space.

## Abstract

We define certain extensions of Jacobi groups of $A_1$, prove an analogue of Chevalley theorem for their invariants, and construct a Dubrovin-Frobenius structure on its orbit space.