Classification of Surfaces of Revolution According to Gaussian Curvature
Overview1
Rotational surfaces are classified into three types according to the sign of the Gaussian curvature. Within each classification, surfaces with the same curvature share the same local intrinsic characteristics, even though they might have different global, extrinsic properties. In other words, they are locally isometric.
Richard S. Millman and George D. Parker, Elements of Differential Geometry (1977), p153-154 ↩︎