Stationary rotating surfaces in Euclidean 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 ...

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

Embeddings of Surfaces in Euclidean Three-space

Smooth surfaces in three-dimensional Euclidean space

are locally described by classical differential geometry. In case some spatial direction (e.g., the direction of gravity in the natural landscape or the viewing direction in visual space) assumes a special role, this formalism has to be replaced by the special theory of “topographic surfaces’’ and one speaks of “surface relief ’’ (Liebmann, 1902/1927). Examples include topographic relief and— i...