Gauss map

Hello, you have come here looking for the meaning of the word Gauss map. In DICTIOUS you will not only get to know all the dictionary meanings for the word Gauss map, but we will also tell you about its etymology, its characteristics and you will know how to say Gauss map in singular and plural. Everything you need to know about the word Gauss map you have here. The definition of the word Gauss map will help you to be more precise and correct when speaking or writing your texts. Knowing the definition ofGauss map, as well as those of other words, enriches your vocabulary and provides you with more and better linguistic resources.

English

A Gauss map matches each point on the surface (left) with the point on the unit sphere (right) representing the orthogonal vector at said point.
English Wikipedia has an article on:
Wikipedia

Etymology

Named after German mathematician Carl Friedrich Gauss.

Noun

Gauss map (plural Gauss maps)

  1. (geometry, differential geometry) 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.
    • 1969 , 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 -space is equal to the degree of the Gauss map of the surface, multiplied by (the Euclidean volume of the unit -sphere).
    • 2005, F. L. Zak, Tangents and Secants of Algebraic Varieties, American Mathematical Society, page 5:
      In §2 we use results of §1 for the study of Gauss maps of projective varieties. The classical Gauss map associates to each point of a nonsingular real affine hypersurface the unit vector of the external normal at this point.

See also

Further reading