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

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dc.creatorGrinberg, Eric L.
dc.creatorHaizhong, Li
dc.date2007-07-12
dc.date.accessioned2026-07-07T08:16:18Z
dc.date.available2026-07-07T08:16:18Z
dc.descriptionIn 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 χ(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 $a$ is a fixed unit vector. Grotemeyer showed that the total integral of this integrand is (2/3)pi times chi(M). We generalize Grotemeyer's result to oriented closed even-dimesional hypersurfaces of dimension n in an (n+1) ndimensional space form N^{n+1}(k).
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/0707.1860
dc.identifierhttp://arxiv.org/abs/0707.1860
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/133734
dc.subjectDifferential Geometry
dc.subject53C42; 53A10
dc.titleThe Gauss-Bonnet-Grotemeyer Theorem in spaces of constant curvature
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