Ruled surfaces in Lorentz-Minkowski 3-spaces with non-degenerate second fundamental form.
Yoon, Dae Won (2006)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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Yoon, Dae Won (2006)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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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...
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.
Abdel-Baky, R.A., Abd-Ellah, H.N. (2008)
Archivum Mathematicum
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Rashad A. Abdel-Baky, H. N. Abd-Ellah (2008)
Archivum Mathematicum
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In this paper, we study a spacelike (timelike) ruled W-surface in Minkowski 3-space which satisfies nontrivial relation between elements of the set , where and are the Gaussian and mean curvatures of the first and second fundamental forms, respectively. Finally, some examples are constructed and plotted.
Rashad A. Abdel-Baky, H. N. Abd-Ellah (2008)
Archivum Mathematicum
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In this paper, we study a spacelike (timelike) ruled W-surface in Minkowski 3-space which satisfies nontrivial relation between elements of the set , where and are the Gaussian and mean curvatures of the first and second fundamental forms, respectively. Finally, some examples are constructed and plotted.
İyigün, Esen, Arslan, Kadri, Öztürk, Günay (2008)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Bang-Yen Chen (2009)
Open Mathematics
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Submanifolds with parallel mean curvature vector play important roles in differential geometry, theory of harmonic maps as well as in physics. Spatial surfaces in 4D Lorentzian space forms with parallel mean curvature vector were classified by B. Y. Chen and J. Van der Veken in [9]. Recently, spatial surfaces with parallel mean curvature vector in arbitrary pseudo-Euclidean spaces are also classified in [7]. In this article, we classify spatial surfaces with parallel mean curvature vector...
Vladimír Fiřt (1974)
Aplikace matematiky
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