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

Cristián U. Sánchez ^[1]
1. [1] CIEM-FaMAF, Argentina
Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 58, Nº. 1, 2017, págs. 53-75
Idioma: inglés
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Resumen
- 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.