Assertion: curvature's curvature | /r/HasProperty | invariant
Facets:
value: under isometries
type: LOCATION
value: under isometric deformations of the surface
type: LOCATION
Source sentences:
text: keywords = "Conformal, Curvature, Invariant",
text: In particular the Gaussian curvature is an invariant of the metric, Gauss's celebrated Theorema Egregium.
text: In fact, an even stronger theorem holds: the Gaussian curvature is invariant under isometries!
text: In particular, the Gaussian curvature is invariant under isometric deformations of the surface.
text: The Gaussian curvature of an embedded smooth surface in R3 is invariant under the local isometries.