Some Remarks on Isoparametric Functions in Closed 4-Manifolds

Minghao Li

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arXiv · 2501.12563

Some Remarks on Isoparametric Functions in Closed 4-Manifolds

Minghao Li

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Abstract

We study transnormal and isoparametric functions on closed Riemannian 4-manifolds and establish fundamental restrictions on their topology and geometry. In particular, we show that such manifolds cannot be endowed with negatively curved metrics, contrasting with known results in the compact simply connected case. Moreover, in certain cases, we provide a description of their fundamental groups. These findings contribute to a better understanding of the global structure of isoparametric foliations.

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Minghao Li. 2025-02-19. Some Remarks on Isoparametric Functions in Closed 4-Manifolds. https://arxiv.org/abs/2501.12563

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