On spherical product surfaces in E3
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Date
2009
Journal Title
Journal ISSN
Volume Title
Publisher
IEEE
Abstract
In the present study we consider spherical product surfaces X = alpha circle times beta of two 2D curves in E-3. We prove that if a spherical product surface patch X = alpha circle times beta has vanishing Gaussian curvature K (i.e. a flat surface) then either alpha or beta is a straight line. Further, we prove that if alpha(u) is a straight line and beta(v) is a 2D curve then the spherical product is a non-minimal and flat surface. We also prove that if beta(v) is a straight line passing through origin and alpha(u) is any 2D curve (which is not a line) then the spherical product is both minimal and flat. We also give some examples of spherical product surface patches with potential applications to visual cyberworlds.
Description
Bu çalışma, 07-11 Eylül 2009 tarihleri arasında Bradford[İngiltere]’da düzenlenen International Conference on Cyberworlds (CW 2009)’da bildiri olarak sunulmuştur.
Keywords
Function based geometry modelling, Minimal surfaces, Spherical product surface, Range, Superquadris, Models, Computer science, Engineering, Robotics, Spheres, Cyberworlds, Flat surfaces, Gaussian curvatures, Minimal surfaces, Potential applications, Product surface, Straight lines, Two dimensional
Citation
Arslan, K. vd. (2009). "On spherical product surfaces in E3". ed. Hassan Ugail. vd. 2009 International Conference on Cyberworlds, 132-137.