Gauss map

In differential geometry, the Gauss map (named, like so many things, after Carl F. Gauss) maps a surface in Euclidean space R3 to the unit sphere S^2. Namely, given a surface S lying in R3, the Gauss map is a continuous map N:S o S^2 such that N(p) is orthogonal to S at p.

Related Topics:
Differential geometry - So many things - Carl F. Gauss - Surface - Euclidean space

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The Gauss map can be defined (globally) if and only if the surface is orientable, but it is always defined locally (i.e. on a small piece of the surface). The Jacobian of the Gauss map is equal to Gauss curvature, and the differential of the Gauss map is called the shape operator.

Related Topics:
Orientable - Jacobian - Gauss curvature - Differential - Shape operator

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