Quaternionic representation of the moving frame for surfaces in Euclidean three-space and Lax pair.

Bracken, Paul

Displaying similar documents to “Quaternionic representation of the moving frame for surfaces in Euclidean three-space and Lax pair.”

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...

Polynomial translation surfaces of Weingarten types in Euclidean 3-space

Dae Yoon (2010)

Open Mathematics

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In this paper, we classify polynomial translation surfaces in Euclidean 3-space satisfying the Jacobi condition with respect to the Gaussian curvature, the mean curvature and the second Gaussian curvature.

Space-like Weingarten surfaces in the three-dimensional Minkowski space and their natural partial differential equations

Georgi Ganchev, Vesselka Mihova (2013)

Open Mathematics

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On any space-like Weingarten surface in the three-dimensional Minkowski space we introduce locally natural principal parameters and prove that such a surface is determined uniquely up to motion by a special invariant function, which satisfies a natural non-linear partial differential equation. This result can be interpreted as a solution to the Lund-Regge reduction problem for space-like Weingarten surfaces in Minkowski space. We apply this theory to linear fractional space-like Weingarten...