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arXiv · 2404.02050

Classification of superpotentials for cohomogeneity one Ricci solitons

Qiu Shi Wang
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Abstract

We classify superpotentials for the Hamiltonian system corresponding to the cohomogeneity one gradient Ricci soliton equations. Aside from recovering known examples of superpotentials for steady solitons, we find a new superpotential on a specific case of the B\'erard Bergery-Calabi ansatz. The latter is used to obtain an explicit formula for a steady complete soliton with an equidistant family of hypersurfaces given by circle bundles over $S^2\times S^2$. There are no superpotentials in the non-steady case in dimensions greater than 2, even if polynomial coefficients are allowed. We also briefly discuss generalised first integrals and the limitations of some known methods of finding them.

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Qiu Shi Wang. 2024-04-02. Classification of superpotentials for cohomogeneity one Ricci solitons. https://doi.org/10.1016/j.geomphys.2024.105294

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