# Bihamiltonian Cohomologies and Integrable Hierarchies II: the Tau Structures

## TL;DR

This paper explores the relationship between bihamiltonian structures, Frobenius manifolds, and tau structures, classifying deformations of integrable hierarchies with tau structures to deepen understanding of their geometric and algebraic properties.

## Contribution

It introduces a classification of deformations of principal hierarchies with tau structures derived from bihamiltonian structures of hydrodynamic type.

## Key findings

- Established a connection between bihamiltonian structures and Frobenius manifolds.
- Classified deformations of principal hierarchies with tau structures.
- Provided a framework for understanding integrable hierarchies via geometric structures.

## Abstract

Starting from a so-called flat exact semisimple bihamiltonian structures of hydrodynamic type, we arrive at a Frobenius manifold structure and a tau structure for the associated principal hierarchy. We then classify the deformations of the principal hierarchy which possess tau structures.