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math.DG2025
Hessian geometry and Frobenius manifolds with curvature
Andreas Vollmer
A Hessian manifold is a Riemannian manifold such that, locally, the metric can be written as the Hessian of a function, which is called the Hessian potential. A Curved Frobenius ma…
math.DG2025
Affine hypersurfaces and superintegrable systems
Vicente Cortés, Andreas Vollmer
It was recently shown that under mild assumptions second-order conformally superintegrable systems can be encoded in a -tensor, called structure tensor. For abundant systems…
math.DG2024
Manifolds with a commutative and associative product structure that encodes superintegrable Hamiltonian systems
Andreas Vollmer
We show that two natural and a priori unrelated structures encapsulate the same data, namely certain commutative and associative product structures and a class of superintegrable H…