Courbures intrinsèques dans les catégories analytico-géométriques
[Intrinsic curvatures in analytic-geometric categories]
Annales de l'Institut Fourier, Volume 53 (2003) no. 6, pp. 1897-1924.

Two types of curvatures are associated to a compact, definable subset of a real analytic Riemannian manifold. If the manifold has constant curvature, there are some linear relations between these measures. As application, a kinematic formula is proved, local densities are defined and volumes of regular simplexes are studied.

Deux types de courbures sont associés à un sous-ensemble compact et définissable d'une variété riemannienne analytique réelle. Si la variété est de courbure constante, il y a des relations linéaires entre ces mesures. Comme application, nous démontrons une formule cinématique, définissons des densités locales, et nous étudions les volumes des simplexes réguliers.

DOI: 10.5802/aif.1995
Classification: 53C65,  14P10
Keywords: curvatures, subanalytic spaces, kinematic formula, densities
Bernig, Andreas 1; Bröcker, Ludwig 2

1 Universität Freiburg, Institut für Mathematik, Eckerstr. 1, 79104 Freiburg (Allemagne)
2 Universität Münster, SFB-47 Geometrische Strukturen, Hittorfstr. 27, 48149 Münster (Allemagne)
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Bernig, Andreas; Bröcker, Ludwig. Courbures intrinsèques dans les catégories analytico-géométriques. Annales de l'Institut Fourier, Volume 53 (2003) no. 6, pp. 1897-1924. doi : 10.5802/aif.1995. http://www.numdam.org/articles/10.5802/aif.1995/

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