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arXiv · 2410.21016

The Equivalence of the Existences of Transnormal and Isoparametric Functions on Compact Manifolds

Minghao Li·Ling Yang
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Abstract

Through exploring the embedded transnormal systems of codimension 1, we show the existence of a transnormal function on a connected complete Riemannian manifold requires the underlying manifold to have a vector bundle structure or a linear double disk bundle decomposition. Conversely, any smooth manifold with either of these structures can be endowed with a Riemannian metric so that it admits a transnormal function, which, under suitable compactness conditions, can become isoparametric. As a corollary, for compact manifolds, the existences of transnormal and isoparametric functions impose the same topological constraints.

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Minghao Li, Ling Yang. 2024-10-28. The Equivalence of the Existences of Transnormal and Isoparametric Functions on Compact Manifolds. https://arxiv.org/abs/2410.21016

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