Courbures intrinsèques dans les catégories analytico-géométriques  [ Intrinsic curvatures in analytic-geometric categories ]
Annales de l'Institut Fourier, Volume 53 (2003) no. 6, p. 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 : https://doi.org/10.5802/aif.1995
Classification:  53C65,  14P10
Keywords: curvatures, subanalytic spaces, kinematic formula, densities
@article{AIF_2003__53_6_1897_0,
     author = {Bernig, Andreas and Br\"ocker, Ludwig},
     title = {Courbures intrins\`eques dans les cat\'egories analytico-g\'eom\'etriques},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {53},
     number = {6},
     year = {2003},
     pages = {1897-1924},
     doi = {10.5802/aif.1995},
     zbl = {1053.53053},
     mrnumber = {2038783},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_2003__53_6_1897_0}
}
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/item/AIF_2003__53_6_1897_0/

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