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Displaying similar documents to “On related vector fields of capillary surfaces.”

On superminimal surfaces

Thomas Friedrich (1997)

Archivum Mathematicum

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Using the Cartan method O. Boruvka (see [B1], [B2]) studied superminimal surfaces in four-dimensional space forms. In particular, he described locally the family of all superminimal surfaces and classified all of them with a constant radius of the indicatrix. We discuss the mentioned results from the point of view of the twistor theory, providing some new proofs. It turns out that the superminimal surfaces investigated by geometers at the beginning of this century as well...

Application of spaces of subspheres to conformal invariants of curves and canal surfaces

Rémi Langevin, Jun O'Hara, Shigehiro Sakata (2013)

Annales Polonici Mathematici

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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...