Developable surfaces in Euclidean space

Characterizations of Slant Ruled Surfaces in the Euclidean 3-space

In this study, we give the relationships between the conical curvatures of ruled surfaces generated by the unit vectors of the ruling, central normal and central tangent of a ruled surface in the Euclidean 3-space E^3. We obtain differential equations characterizing slant ruled surfaces and if the reference ruled surface is a slant ruled surface, we give the conditions for the surfaces generate...

Minimal Surfaces in Euclidean Space

Deforming Developable Surfaces

One of the techniques in digital geometry processing that has been studied for many years is mesh deformation. Recently, researchers have proposed deformation methods that preserve certain aspects of the mesh, such as geometric features and material properties. In this project we look at preserving developability of a surface. Specifically, if it is known that a surface is developable before de...

Embeddings of Surfaces in Euclidean Three-space

Stationary rotating surfaces in Euclidean space

A stationary rotating surface is a compact surface in Euclidean space whose mean curvature H at each point x satisfies 2H(x) = ar + b, where r is the distance from x to a fixed straightline L, and a and b are constants. These surfaces are solutions of a variational problem that describes the shape of a drop of incompressible fluid in equilibrium by the action of surface tension when it rotates ...