By Eric Grinberg and Li Haizhong

In 1963, K.P.Grotemeyer proved an interesting variant of the Gauss-Bonnet Theorem. Let M be an oriented closed surface in the Euclidean space R^3 with Euler characteristic \chi(M), Gauss curvature G and unit normal vector field n. Grotemeyer's identity replaces the Gauss-Bonnet integrand G by the normal moment <a,n>^2G, where *a*... Show more

July 12, 2007

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The Gauss-Bonnet-Grotemeyer Theorem in spaces of constant curvature

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