Connectedness of the algebraic set of vectors generating planar normal sections of homogeneous isoparametric hypersurfaces - Sanchez, Cristian Urbano (2017)
Let M Sn+1 Rn+2 be a homogeneous isoparametric hypersurfaceand consider the algebraic set of unit tangent vectors generating planarnormal sections at a point E 2 M (denoted by bXE [M] TE (M)). Th epresent paper is devoted to prove that bXE [M] is connected by arcs.. This in turn proves that its projective image X [M] RP (TE (M)) also has this property.