Gauss map

Etymology
Named after German mathematician.

Noun

 * 1)  A map from a given oriented surface in Euclidean space to the unit sphere which maps each point on the surface to a unit vector orthogonal to the surface at that point.
 * 2) * 1969 [Van Nostrand],, A Survey of Minimal Surfaces, 2014, Dover, Unabridged republication, page 73,
 * There exist complete generalized minimal surfaces, not lying in a plane, whose Gauss map lies in an arbitrarily small neighborhood on the sphere.
 * 1) * 1985, R. G. Burns (translator), B. A. Dubrovin,, , Modern Geometry― Methods and Applications: Part II: The Geometry and Topology of Manifolds, Springer, , page 114,
 * 14.2.2 Theorem The integral of the Gaussian curvature over a closed hypersurface in Euclidean $$n$$-space is equal to the degree of the Gauss map of the surface, multiplied by $$\gamma_n$$ (the Euclidean volume of the unit $$(n-1)$$-sphere).