Isoparametric foliations and complex structures
Chao Qian, Zizhou Tang, Wenjiao Yan · International Journal of Mathematics · 2026
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 [Formula: see text], [Formula: see text] in the unit sphere, as well as on focal submanifolds [Formula: see text] of OT-FKM type with [Formula: see text], [Formula: see text] and [Formula: see text] in the definite case. Furthermore, we investigate the existence and non-existence of invariant (almost) complex structures on homogeneous isoparametric hypersurfaces with [Formula: see text], providing a complete classification of those that admit such structures. Finally, we discuss the geometric properties of the complex structures arising from isoparametric theory.