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f-Eikonal helix submanifolds and f-Eikonal helix curves
Helix submanifold Eikonal function Helix line
2012/6/15
Let M{\subset}\mathbb{R}^{n} be a Riemannian helix submanifold with respect to the unit direction d{\in}\mathbb{R}^{n} and f:M{\to}\mathbb{R} be a eikonal function. We say that M is a f-eikonal helix ...
Non-isoparametric solutions of the eikonal equation
Non-isoparametric solutions eikonal equation
2010/12/3
In this paper, we prove that a quartic solution of the eikonal equation |∇xf|2 = 16x6 in Rn is either isoparametric or congruent to a polynomial f = (Pn i=1 x2 i )2 − 8(Pk i=1 x2 i )(Pn
i...
Solutions Near Singular Points to the Eikonal and Related First Order Non-linear Partial Differential Equations in Two Independent Variables
Singular Points Eikonal Partial Differential Equations
2010/11/1
A detailed study of solutions to the first order partial differential equation H(x,y,z_x,z_y)=0, with special emphasis on the eikonal equation z_x^2+z_y^2=h(x,y), is made near points where the equatio...