Displaying similar documents to “A geometric characterization of helicoidal surfaces of constant mean curvature.”

The PDE describing constant mean curvature surfaces

Hongyou Wu (2001)

Mathematica Bohemica

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We give an expository account of a Weierstrass type representation of the non-zero constant mean curvature surfaces in space and discuss the meaning of the representation from the point of view of partial differential equations.

Invariants and Bonnet-type theorem for surfaces in ℝ4

Georgi Ganchev, Velichka Milousheva (2010)

Open Mathematics

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In the tangent plane at any point of a surface in the four-dimensional Euclidean space we consider an invariant linear map ofWeingarten-type and find a geometrically determined moving frame field. Writing derivative formulas of Frenet-type for this frame field, we obtain eight invariant functions. We prove a fundamental theorem of Bonnet-type, stating that these eight invariants under some natural conditions determine the surface up to a motion. We show that the basic geometric classes...

Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature

Rafael López, Esma Demir (2014)

Open Mathematics

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We classify all helicoidal non-degenerate surfaces in Minkowski space with constant mean curvature whose generating curve is a the graph of a polynomial or a Lorentzian circle. In the first case, we prove that the degree of the polynomial is 0 or 1 and that the surface is ruled. If the generating curve is a Lorentzian circle, we prove that the only possibility is that the axis is spacelike and the center of the circle lies on the axis.