A generalization of Cartan’s theorem on isoparametric cubics

DOI10.1090/S0002-9939-10-10385-2zbMath1194.53052arXiv1001.2387OpenAlexW3098222114MaRDI QIDQ3581110

Vladimir G. Tkachev

Publication date: 16 August 2010

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.2387

zbMATH Keywords

division algebraseiconal equationquadratic mapsCartan's theoremcomposition formulasminimal cubic cones

Mathematics Subject Classification ID

Nonlinear first-order PDEs (35F20) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Quadratic and bilinear forms, inner products (15A63) Composition algebras (17A75) Nonassociative division algebras (17A35)

Related Items (7)

Minimal cubic cones via Clifford algebras ⋮ New explicit solutions to the \(p\)-Laplace equation based on isoparametric foliations ⋮ A Jordan algebra approach to the cubic eiconal equation ⋮ Biharmonic homogeneous polynomial maps between spheres ⋮ Harmonic cubic homogeneous polynomials such that the norm-squared of the Hessian is a multiple of the Euclidean quadratic form ⋮ A note on isoparametric polynomials ⋮ On the non-vanishing property for real analytic solutions of the $p$-Laplace equation

Cites Work

• Compositions of quadratic forms
• Quadratic forms between Euclidean spheres
• Remarks on closed minimal submanifolds in the standard Riemannian m- sphere
• Polynomial maps from spheres to spheres
• Complete minimal surfaces in \(S^ 3\)
• Sur des familles remarquables d'hypersurfaces isoparametriques dans les espaces spheriques

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