Isoparametric foliations and complex structures

doi:10.1142/s0129167x26500400

Isoparametric foliations and complex structures

2026-04-01

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DOI：10.1142/s0129167x26500400

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Explicit representations of complex structures on closed manifolds are valuable, but relatively rare in the literature. By 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.

Keywords:

Isoparametric foliation

complex structure

Isoparametric foliations and complex structures

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