On the topology of isoparametric hypersurfaces with four distinct principal curvatures
On the topology of isoparametric hypersurfaces with four distinct principal curvatures
Let $(m_-,m_+)$ be the pair of multiplicities of an isoparametric hypersurface in the unit sphere $S^{n+1}$ with four distinct principal curvatures —w.r.g., we assume that $m_-\le m_+$. In the present paper we prove that, in the case 4B2 of U. Abresch (Math. Ann. 264 (1983), 283–302) (i.e., where $3m_-=2(m_++1)$), $m_-$ …