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<p>For two generalized Frobenius manifolds related by a Legendre-type transformation, we show that the associated integrable hierarchies of hydrodynamic type, which are called the Legendre-extended Principal Hierarchies, are related by a certain linear reciprocal transformation; we also show, under the semisimplicity condition, that the topological deformations of these Legendre-extended Principal Hierarchies are related by the same linear reciprocal transformation.</p>

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Legendre Transformations of a Class of Generalized Frobenius Manifolds and the Associated Integrable Hierarchies

  • 期刊论文

  • 发表日期：

    2025年5月7日

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  • Si-Qi Liu,
  • Haonan Qu,
  • Youjin Zhang

摘要

For two generalized Frobenius manifolds related by a Legendre-type transformation, we show that the associated integrable hierarchies of hydrodynamic type, which are called the Legendre-extended Principal Hierarchies, are related by a certain linear reciprocal transformation; we also show, under the semisimplicity condition, that the topological deformations of these Legendre-extended Principal Hierarchies are related by the same linear reciprocal transformation.