A cellular parametrization for closed surfaces with a distinguished point.
Näätänen, Marjatta (1993)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Displaying similar documents to “Foliations by surfaces of a peculiar class”
A cellular parametrization for closed surfaces with a distinguished point.
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Branch Points of Conformal Mappings of Surfaces.
J. Eschenburg, R. Tribuzy (1987/88)
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We review some techniques from the Möbius geometry of curves and surfaces in the 3-sphere, consider canal surfaces using their characteristic circles, and express the conformal curvature, and conformal torsion, of a vertex-free space curve in terms of its corresponding curve of osculating circles, and osculating spheres, respectively. We accomplish all of this strictly within the framework of Möbius geometry, and compare our results with the literature. Finally, we show how our formulation...
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Elmar Vogt (1973)
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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...
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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...
The conformal structure of Riemann surfaces with boundary parametrizing minimal surfaces.
Reinhold Böhme (1986/87)
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Surfaces with parallel second fundamental form in Bianchi-Cartan-Vranceanu spaces
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We give a complete classification of surfaces with parallel second fundamental form in 3-dimensional Bianchi-Cartan-Vranceanu spaces.
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The PDE describing constant mean curvature surfaces
Hongyou Wu (2001)
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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.