Theorema Egregium

From Diffgeom
Jump to: navigation, search


Gauss's Theorema Egregium or Gauss's Remarkable Theorem states that the Gaussian curvature of a surface embedded in \R^3 is invariant under isometries. In other words, the Gaussian curvature is intrinsic to the geometry of the surface and is independent of the manner in which the surface is embedded in \R^3.