noun
Meaning 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.
Definition source: English Wiktionary via Wiktextract
Qualifier: differential geometry
Topics: geometry, mathematics, sciences
Examples
- 1969 [Van Nostrand], Robert Osserman, 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.
- 1985, R. G. Burns (translator), B. A. Dubrovin, A. T. Fomenko, S. P. Novikov, Modern Geometry― Methods and Applications: Part II: The Geometry and Topology of Manifolds, Springer, Graduate Texts in Mathematics, 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 γn (the Euclidean volume of the unit (n-1)-sphere).
Meaning relationships
Synonyms: none provided
Antonyms: none provided