Gauß Curvature Surfaces

Surfaces of constant or prescribed Gauß curvature. The Gauß curvature K of a smooth surface in R3 is the product of the two principal curvature values, and belongs to the intrinsic geometry of the surface. Ruled surfaces have zero Gauß curvature. Surfaces with constant negative Gauß curvature cannot be immersed into R3 as complete surfaces.


  1. Manfredo P. do Carmo: Differential Geometry of Curves and Surfaces, Prentice-Hall Englewood Cliffs, NJ (1976).
  2. Gerd Fischer: Mathematical Models, Vieweg Verlag (1986).
  3. Alfred Gray: Modern Differential Geometry of Curves and Surfaces, CRC Press (1994).

Technical Note

As a guide, meshes should have no holes, no degenerate triangles and elements, no duplicate vertices. Surfaces should have meshes with an adjacency relation.