Planar normal sections of focal manifolds of isoparametric hypersurfaces in spheres

• Cristián U. Sánchez ^[1]
  1. [1] Universidad Nacional de Córdoba

     Universidad Nacional de Córdoba

     Argentina

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 56, Nº. 2, 2015, págs. 119-133
• Idioma: inglés
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• Resumen

  • The present paper contains some results about the algebraic sets of planar normal sections associated to the focal manifolds of homogeneous isoparametric hypersurfaces in spheres. With the usual identification of the tangent spaces to the focal manifold with subspaces of the tangent spaces to the isoparametric hypersurface, it is proven that the algebraic set of planar normal sections of the focal manifold is contained in that of the original hypersurface.