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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Näätänen, Marjatta (1993)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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H. G. Helfenstein, E. Katz (1972)
Compositio Mathematica
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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...
Alois Švec (1966)
Czechoslovak Mathematical Journal
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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...
Sharma, Ramesh (1989)
International Journal of Mathematics and Mathematical Sciences
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Marian Munteanu, Ana Nistor (2011)
Open Mathematics
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In the present paper we classify all surfaces in 3 with a canonical principal direction. Examples of this type of surfaces are constructed. We prove that the only minimal surface with a canonical principal direction in the Euclidean space 3 is the catenoid.
J. Eschenburg, R. Tribuzy (1987/88)
Mathematische Annalen
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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...