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arXiv · 2502.09041

Isoparametric foliations and complex structures

Chao Qian·Zizhou Tang·Wenjiao Yan
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Abstract

Explicit representations of complex structures on closed manifolds are valuable, but relatively rare in the literature. Using isoparametric theory, we construct complex structures on isoparametric hypersurfaces with $g=4, m=1$ in the unit sphere, as well as on focal submanifolds $M_+$ of OT-FKM type with $g=4$, $m=2$ and $m=4$ in the definite case. Furthermore, we investigate the existence and non-existence of invariant (almost) complex structures on homogeneous isoparametric hypersurfaces with $g=4$, providing a complete classification of those that admit such structures. Finally, we discuss the geometric properties of the complex structures arising from isoparametric theory.

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Chao Qian, Zizhou Tang, Wenjiao Yan. 2025-02-13. Isoparametric foliations and complex structures. https://arxiv.org/abs/2502.09041

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