Geometry and Topology Seminar: Inhomogeneous isoparametric hypersurfaces of OT-FKM-type in the pseudo-sphere

Abstract: We study isoparametric hypersurfaces, whose principal curvatures are all constant, in the pseudo-Riemannian space forms, especially in the pseudo-sphere $S^{2l-1}_{s}$. A connected submanifold $L$ of $S^{2l-1}_{s}$ is homogeneous if a Lie subgroup of the isometry group of $S^{2l-1}_{s}$ acts on $L$ transitively. In this talk, we show that (connected) isoparametric hypersurfaces of OT-FKM-type and each connected component of its focal variety in $S^{2l-1}_{s}$ are inhomogeneous if the signature $(m, r)$ of its Clifford system satisfies $m\equiv 0\ (\mathrm{mod}\ 4)$ and $r\equiv 0\ (\mathrm{mod}\ 2)$.

Host: Quo-Shin Chi