Resumen de Connectedness of the algebraic set of vectors generating planar normal sections of homogeneous isoparametric hypersurfaces

Cristián U. Sánchez

• Let M⊂Sn+1⊂ Rn+2 be a homogeneous isoparametric hypersurface and consider the algebraic set of unit tangent vectors generating planar normal sections at a point E∈M(denoted by ˆXE[M]⊂TE(M)). The present paper is devoted to prove that ˆXE[M] is connected by arcs. This in turn proves that its projective image X[M]⊂RP(TE(M)) also has this property.