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.
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.
Mot clés : courbures, espaces sous-analytiques, formule cinématique, densités
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},
pages = {1897--1924},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {53},
number = {6},
year = {2003},
doi = {10.5802/aif.1995},
mrnumber = {2038783},
zbl = {1053.53053},
language = {fr},
url = {http://archive.numdam.org/articles/10.5802/aif.1995/}
}
TY - JOUR AU - Bernig, Andreas AU - Bröcker, Ludwig TI - Courbures intrinsèques dans les catégories analytico-géométriques JO - Annales de l'Institut Fourier PY - 2003 SP - 1897 EP - 1924 VL - 53 IS - 6 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1995/ DO - 10.5802/aif.1995 LA - fr ID - AIF_2003__53_6_1897_0 ER -
%0 Journal Article %A Bernig, Andreas %A Bröcker, Ludwig %T Courbures intrinsèques dans les catégories analytico-géométriques %J Annales de l'Institut Fourier %D 2003 %P 1897-1924 %V 53 %N 6 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.1995/ %R 10.5802/aif.1995 %G fr %F AIF_2003__53_6_1897_0
Bernig, Andreas; Bröcker, Ludwig. Courbures intrinsèques dans les catégories analytico-géométriques. Annales de l'Institut Fourier, Tome 53 (2003) no. 6, pp. 1897-1924. doi : 10.5802/aif.1995. http://archive.numdam.org/articles/10.5802/aif.1995/
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