Triality and the normal sections of Cartan’s isoparametric hypersurfaces.

SANCHEZ CRISTIÁN URBANO

REVISTA DE LA UNIóN MATEMáTICA ARGENTINA

UNION MATEMATICA ARGENTINA

Lugar: Bahía Blanca; Año: 2011 vol. 52 p. 73 - 88

0041-6932

The present paper is devoted to study the algebraic sets of nor-mal sections of the so called Cartan’s isoparametric hypersurfaces MR,MC, MH and MO of complete ‡ags in the projective planes RP2, CP2,HP2 and OP2. It presents a connection between ”normed trialities”and the polynomial de…ning the algebraic sets of normal sections ofthese hypersurfaces. It contains also a geometric and topological de-scription of these algebraic sets by means of the isotropy actions ofthe isoparametric hypersurfaces.