Courbures intrinsèques dans les catégories analytico-géométriques
Annales de l'Institut Fourier, Tome 53 (2003) no. 6, p. 1897-1924
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.
DOI : https://doi.org/10.5802/aif.1995
Classification:  53C65,  14P10
Mots clés: courbures, espaces sous-analytiques, formule cinématique, densités
@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://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, Tome 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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