Ruled quartic surfaces, models and classification
نویسندگان
چکیده
منابع مشابه
Ruled Quartic Surfaces, Models and Classification
New historical aspects of the classification, by Cayley and Cremona, of ruled quartic surfaces and the relation to string models and plaster models are presented. In a ‘modern’ treatment of the classification of ruled quartic surfaces the classical one is corrected and completed. A conceptual proof is presented of a result of Rohn concerning curves in P × P of bi-degree (2, 2). The string model...
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Given a surface or scattered data points from a surface in 3-space, we show how to approximate the given data by a ruled surface in tensor product B-spline representation. This leads us to a general framework for approximation in line space by local mappings from the Klein quadric to Euclidean 4-space. The presented algorithm for approximation by ruled surfaces possesses applications in archite...
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A Laguerre minimal surface is an immersed surface in R being an extremal of the functional ∫ (H/K− 1)dA. In the present paper, we prove that any ruled Laguerre minimal surface distinct from a plane is up to motion a convolution of the helicoid x = y tan z, the cycloid r(t) = (t− sin t, 1−cos t, 0) and the Plücker conoid (ax+ by) = z(x+y) for some a, b ∈ R. To achieve invariance under Laguerre t...
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If a normal quartic surface admits a singular point that is not a rational double point, then the surface is determined by the triplet (M,D,E) consisting of the minimal desingularization M , the pullback D of a general hyperplane section, and a non-zero effective anti-canonical divisor E of M . Geometric constructions of all the possible triplets (M,D,E) are given.
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ژورنال
عنوان ژورنال: Geometriae Dedicata
سال: 2010
ISSN: 0046-5755,1572-9168
DOI: 10.1007/s10711-010-9500-0