An alternative moving frame for tubular surfaces around time-like curves in the Minkowski 3-space.
Karacan, Murat Kemal, Bukcu, Bahaddin (2007)
Balkan Journal of Geometry and its Applications (BJGA)
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Karacan, Murat Kemal, Bukcu, Bahaddin (2007)
Balkan Journal of Geometry and its Applications (BJGA)
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Hari das Bagchi, Biswarup Mukherji (1952)
Rendiconti del Seminario Matematico della Università di Padova
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Dreibelbis, D. (2003)
Advances in Geometry
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Orbay, Keziban, Kasap, Emin, Aydemir, İsmail (2009)
Mathematical Problems in Engineering
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Izumiya, Shyuichi, Takeuchi, Nobuko (2003)
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...
J.-H. Chuang, Ch. M. Hoffmann (1992)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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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.
Ulmet, Dan-Eugen (2004)
International Journal of Mathematics and Mathematical Sciences
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Benz, Walter (2000)
Beiträge zur Algebra und Geometrie
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Roussos, Ioannis M. (1988)
Publications de l'Institut Mathématique. Nouvelle Série
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J. Carter, Masahico Saito (1998)
Banach Center Publications
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A necessary and sufficient condition for an immersed surface in 3-space to be lifted to an embedding in 4-space is given in terms of colorings of the preimage of the double point set. Giller's example and two new examples of non-liftable generic surfaces in 3-space are presented. One of these examples has branch points. The other is based on a construction similar to the construction of Giller's example in which the orientation double cover of a surface with odd Euler characteristic...