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J Dorfmeister, E Neher (1985)
Isoparametric hypersurfaces, case $$g=6,\;m=1$$ g = 6 , m = 1Comm. Algebra, 13
Q. Chi (2010)
Isoparametric hypersurfaces with four principal curvatures, IINagoya Mathematical Journal, 204
H. Münzner (1980)
Isoparametrische Hyperflächen in SphärenMathematische Annalen, 251
E. Cartan (1939)
Sur des familles remarquables d'hypersurfaces isoparamétriques dans les espaces sphériquesMathematische Zeitschrift, 45
J. Ritt (1923)
Permutable rational functionsTransactions of the American Mathematical Society, 25
H. Ozeki, M. Takeuchi (1975)
ON SOME TYPES OF ISOPARAMETRIC HYPERSURFACES IN SPHERES ITohoku Mathematical Journal, 27
Dirk Ferus, H. Karcher, H. Münzner (1981)
Cliffordalgebren und neue isoparametrische HyperflächenMathematische Zeitschrift, 177
-. Chi (2011)
ISOPARAMETRIC HYPERSURFACES WITH FOUR PRINCIPAL CURVATURES, III
U. Abresch (1983)
Isoparametric hypersurfaces with four or six distinct principal curvaturesMathematische Annalen, 264
(2012)
The isoparametric story. ncts/tpe 2012 geometry summer course
Qi-Ming Wang (1987)
Isoparametric functions on Riemannian manifolds. IMathematische Annalen, 277
Thomas Cecil, Q. Chi, G. Jensen (2004)
Isoparametric Hypersurfaces with Four Principal CurvaturesAnnals of Mathematics, 166
V. Tkachev (2012)
A Jordan algebra approach to the cubic eiconal equationJournal of Algebra, 419
D. Chang, B. Li (2012)
Description of Entire Solutions of Eiconal Type EquationsCanadian Mathematical Bulletin, 55
V. Tkachev (2010)
A generalization of Cartan's theorem on isoparametric cubicsarXiv: Differential Geometry, 138
E. Cartan (1938)
Familles de surfaces isoparamétriques dans les espaces à courbure constanteAnnali di Matematica Pura ed Applicata, 17
J. Dorfmeister, E. Neher (1985)
Isoparametric hypersurfaces, case g=6, m=1Communications in Algebra, 13
D Khavinson (1995)
A note on entire solutions of the eiconal [eikonal] equationAm. Math. Monthly, 102
V. Tkachev (2010)
Non-isoparametric solutions of the eikonal equationarXiv: Differential Geometry
R. Miyaoka (2013)
Transnormal functions on a Riemannian manifoldDifferential Geometry and Its Applications, 31
R. Miyaoka (2013)
Isoparametric hypersurfaces with (g;m) = (6;2)Annals of Mathematics, 177
U Abresch (1983)
Isoparametric hypersurfaces with four or six distinct principal curvatures. Necessary conditions on the multiplicitiesMath. Ann., 264
We show that any homogeneous polynomial solution of the eiconal type equation $$|\nabla F(x)|^2=m^2|x|^{2m-2}$$ | ∇ F ( x ) | 2 = m 2 | x | 2 m - 2 , $$m\ge 1$$ m ≥ 1 , is either a radially symmetric polynomial $$F(x)=\pm |x|^{m}$$ F ( x ) = ± | x | m (for even $$m$$ m ’s) or it is a composition of a Chebychev polynomial and a Cartan–Münzner polynomial.
Analysis and Mathematical Physics – Springer Journals
Published: Jan 14, 2014
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