On the Lines of Equidistance of a Family of Surfaces
C. E. Weatherburn (1930)
Journal de Mathématiques Pures et Appliquées
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C. E. Weatherburn (1930)
Journal de Mathématiques Pures et Appliquées
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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.
Karacan, Murat Kemal, Bukcu, Bahaddin (2007)
Balkan Journal of Geometry and its Applications (BJGA)
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Izumiya, Shyuichi, Takeuchi, Nobuko (2003)
Beiträge zur Algebra und Geometrie
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Benz, Walter (2000)
Beiträge zur Algebra und Geometrie
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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...
Ulmet, Dan-Eugen (2004)
International Journal of Mathematics and Mathematical Sciences
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Vladimír Fiřt (1974)
Aplikace matematiky
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Kalikakis, Dimitrios E. (2002)
Abstract and Applied Analysis
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J.-H. Chuang, Ch. M. Hoffmann (1992)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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