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Your search keyword '"Minimal surface of revolution"' showing total 3 results
Start Over Descriptor "Minimal surface of revolution" Publication Year Range Last 10 years
3 results on '"Minimal surface of revolution"'

1. Classifications of Canal Surfaces with the Gauss Maps in Minkowski 3-Space

Author

Xueqian Tian, Xueshan Fu, Young Ho Kim, and Jinhua Qian

Subjects
Surface (mathematics), Pointwise, pseudo sphere, Gauss map, 010308 nuclear & particles physics, General Mathematics, Frenet–Serret formulas, lcsh:Mathematics, 010102 general mathematics, Mathematical analysis, Gauss, lcsh:QA1-939, 01 natural sciences, Laplace operator, Minimal surface of revolution, 0103 physical sciences, Minkowski space, Computer Science (miscellaneous), Computer Science::Programming Languages, 0101 mathematics, Engineering (miscellaneous), Mathematics, canal surface
Abstract

In this work, we study the canal surfaces foliated by pseudo spheres S12 along a Frenet curve in terms of their Gauss maps in Minkowski 3-space. Such kind of surfaces with pointwise 1-type Gauss maps are classified completely. For example, the canal surface with proper pointwise 1-type Gauss map of the first kind if and only if it is a part of a minimal surface of revolution.

Published
2020

2. Digital Surface of Revolution with Hand-Drawn Generatrix

Author

Gaëlle Largeteau-Skapin, Eric Andres, Lydie Richaume, Université de Poitiers, Synthèse et analyse d'images (XLIM-ASALI), XLIM (XLIM), and Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS)-Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Statistics and Probability, Surface (mathematics), Engineering drawing, surface of revolution, 0102 computer and information sciences, 02 engineering and technology, 01 natural sciences, Simple (abstract algebra), Euclidean geometry, 0202 electrical engineering, electronic engineering, information engineering, Calculus, [INFO]Computer Science [cs], digital surfaces, implicit functions, Mathematics, Sequence, Implicit function, Applied Mathematics, Condensed Matter Physics, 010201 computation theory & mathematics, Minimal surface of revolution, Modeling and Simulation, Generatrix, 020201 artificial intelligence & image processing, Geometry and Topology, Computer Vision and Pattern Recognition, Surface of revolution
Abstract

International audience; In this paper we present a simple method to create general 3D digital surfaces of revolution based on a 2D implicit curve of revolution (therefore not limited to a circle) and a hand-drawn generatrix. Our method can handle any sequence of Euclidean 2D points, that represents a curve, as generatrix. One can choose the topology of the surface that may have 1-tunnels, 0-tunnels or no tunnels with applications in 3D printing for instance. An online tool that illustrates the method is proposed.

Published
2017

3. Conformal type of ends of revolution in space forms of constant sectional curvature

Author

Vicent Gimeno and Irmina Gozalbo

Subjects
Mathematics - Differential Geometry, Conformal map, Geometry, 02 engineering and technology, 01 natural sciences, Hyperbolic space, Computer Science::Robotics, Euclidean space, Simply connected space, Parabolicity, FOS: Mathematics, 0202 electrical engineering, electronic engineering, information engineering, Sectional curvature, 0101 mathematics, Primary 53C20, 53C40, Secondary 53C42, Mathematics, Sphere, End of revolution, 010102 general mathematics, Mathematical analysis, 020206 networking & telecommunications, Physics::History of Physics, Differential Geometry (math.DG), Differential geometry, Minimal surface of revolution, Geometry and Topology, Surface of revolution, Analysis, Stochastic completeness
Abstract

In this paper we consider the conformal type (parabolicity or non-parabolicity) of complete ends of revolution immersed in simply connected space forms of constant sectional curvature. We show that any complete end of revolution in the $3$-dimensional Euclidean space or in the $3$-dimensional sphere is parabolic. In the case of ends of revolution in the hyperbolic $3$-dimensional space, we find sufficient conditions to attain parabolicity for complete ends of revolution using their relative position to the complete flat surfaces of revolution., Comment: 22 pages, 5 figures

Published
2016

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