Resumen de Triality and the normal sections of Cartan’s isoparametric hypersurfaces

Cristián Sánchez

• The present paper is devoted to study the algebraic sets of normal sections of the so called Cartan’s isoparametric hypersurfaces MR, MC, MH and MO of complete flags in the projective planes RP2, CP2, HP2 and OP2. It presents a connection between “normed trialities” and the polynomial defining the algebraic sets of normal sections of these hypersurfaces. It contains also a geometric and topological description of these algebraic sets by means of the isotropy actions of the isoparametric hypersurfaces.