Planar normal sections on isoparametric hypersurfaces and the infinity Laplacian

• Julio C. Barros ^[1] ; Cristián U. Sánchez ^[2]
  1. [1] Universidad Nacional de Río Cuarto

     Universidad Nacional de Río Cuarto

     Argentina

     
  2. [2] CIEM - CONICET, Argentina
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 55, Nº. 2, 2014, págs. 107-121
• Idioma: inglés
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• Resumen

  • We present a new characterization of Cartan isoparametric hypersurfaces in terms of properties of the polynomial that determines the algebraic set of planar normal sections on the homogeneous isoparametric hypersurfaces in spheres. We show that Cartan isoparametric hypersurfaces are the only homogeneous isoparametric hypersurfaces in spheres for which the infinity Laplacian of the polynomial that defines the algebraic set of planar normal sections is the polynomial multiplied by the squared norm of the tangent vector. Since it is required for our work, we also give these polynomials for all homogeneous isoparametric hypersurfaces in spheres.