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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.
14.2.2 TheoremThe 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).
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.