Gauss map

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English

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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.
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Etymology

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Named after German mathematician Carl Friedrich Gauss.

Noun

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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 [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 -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

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Further reading

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