Word.ws English Dictionary

Gauss map

Gauss map noun: 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.

gauss map: a map from a given oriented surface in Euclidean space to the unit sphere which maps each point on...
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Noun

Gauss map (plural Gauss maps)

  1. (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.
    • 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).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...

Forms of Gauss map

pluralGauss maps

Origin of Gauss map

Named after German mathematician Carl Friedrich Gauss.

Questions about Gauss map

What does Gauss map mean?
Gauss map means 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.
What part of speech is Gauss map?
Gauss map is a noun.
What is the plural of Gauss map?
The plural of Gauss map is Gauss maps.

Words near Gauss map in the dictionary

  1. gauss
  2. Gauss curvature
  3. Gauss curvatures
  4. Gauss gun
  5. Gauss guns
  6. Gauss map
  7. Gauss maps
  8. Gauss symbol
  9. Gauss's area formula
  10. Gauss-Bonnet theorem
  11. Gauss-Codazzi equation

Source and license

Adapted from Wiktionary: Gauss map (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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