A PLETHORA OF NON-BENDING SURFACES OF REVOLUTION: CLASSIFICATIONS AND EXPLICIT PARAMETERIZATIONS

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.

Automated summary

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.