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Scientific paper ID 996 : 2014/3
MINIMAL GENERALIZED HELICOIDS
Ognian Kassabov Abstract. The generalized helicoids are surfaces that the standart helicoids as well as all surfaces of revolution. A differential equation equivalent to the condition for a geleralized helicoid to be a minimal surface is obtained. When one of the constants in the solution tends to zero the solution of this equation tends to the classical helicoids or classical catenoids.
Минимални повърхнини обобщени хеликоиди.minimal surface generalized helicoid. Ognian Kassabov BIBLIOGRAPHY [1] Eisenhart L., A Treatise on the Differential Geometry of Curves and Surfaces. Ginn and company, Boston, New York, Chicago, London, 1909. [2] Euler, L., Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes sive solutio problematis isoperimetrici latissimo sensu accepti, Opera omni (1) 24, F’ussli Turici, Lausanne, 399-406, 1952 (englsh translation). [3] Gray A., Abbena E., Salomon S., Modern Differential Geometry of Curves and Surfaces with MATHEMATICA. Boca Raton, FL: CRC Press. [4] Meusnier, J.B., Mémiore sur la courbure des surfaces. Mémoires des savans étrangrs 1, 477-510, 1776. [5] Xu, G., Wang, G., Quintic parametric polynomial minimal surfaces and their properties. Differential Geom. Appl. 28, 697–704, 2010. |
