Journal
PROCEEDINGS OF THE TWENTY-SECOND INTERNATIONAL CONFERENCE ON GEOMETRY, INTEGRABILITY AND QUANTIZATION
Volume 22, Issue -, Pages 219-241Publisher
INST BIOPHYSICS & BIOMEDICAL ENGINEERING BULGARIAN ACAD SCIENCES
DOI: 10.7546/giq-22-2021-219-241
Keywords
Axially symmetric surfaces; elliptic integrals; Jacobian elliptic functions; parameterizations; surface geometry
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The article presents highly rich two/three parametric families of non-bending rotational surfaces in the three dimensional Euclidean space, along with their natural classifications and explicit parameterizations. By varying parameters, the evolution of these surfaces can be traced and visualized through their topological transformations, leaving deeper questions about their metrical properties, mechanical applications, etc. for future explorations.
As the title itself suggests here we are presenting extremely reach two/three parametric families of non-bending rotational surfaces in the three dimensional Euclidean space and provide the necessary details about their natural classifications and explicit parameterizations. Following the changes of the relevant parameters it is possible to trace out the evolution of these surfaces and even visualize them through their topological transformations. Many, and more deeper questions about their metrical properties, mechanical applications, etc. are left for future explorations.
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