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arXiv · 1908.05796

Laplacian algebras, manifold submetries and the Inverse Invariant Theory Problem

Ricardo A. E. Mendes·Marco Radeschi
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Abstract

Manifold submetries of the round sphere are a class of partitions of the round sphere that generalizes both singular Riemannian foliations, and the orbit decompositions by the orthogonal representations of compact groups. We exhibit a one-to-one correspondence between such manifold submetries and maximal Laplacian algebras, thus solving the Inverse Invariant Theory problem for this class of partitions. Moreover, a solution to the analogous problem is provided for two smaller classes, namely orthogonal representations of finite groups, and transnormal systems with closed leaves.

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Ricardo A. E. Mendes, Marco Radeschi. 2019-08-15. Laplacian algebras, manifold submetries and the Inverse Invariant Theory Problem. https://arxiv.org/abs/1908.05796

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