23 citations · 220 across the 53 of their papers we have counts for
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Non-isoparametric solutions of the eikonal equation
Vladimir G. Tkachev
In this paper, we prove that a quartic polynomial solution of the eikonal equation in is either an isoparametric polynomial or congruent to a polyn…
On a classification of minimal cubic cones in R^n
Vladimir G. Tkachev
We establish a classification of cubic minimal cones in case of the so-called radial eigencubics. Our principal result states that any radial eigencubic is either a member of the i…
Minimal cubic cones via Clifford algebras
Vladimir G. Tkachev
We construct two infinite families of algebraic minimal cones in . The first family consists of minimal cubics given explicitly in terms of the Clifford systems. We show tha…
A generalization of Cartan's theorem on isoparametric cubics
Vladimir G. Tkachev
We give a generalization of the well-known result of E. Cartan on isoparametric cubics by showing that a homogeneous cubic polynomial solution of the eiconal equation $|\nabla f|^2…