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La géométrie métrique des variétés riemanniennes. (Variations sur la formule \(a^ 2=b^ 2+c^ 2-2bc\,\cos \,\alpha).\) (The metric geometry of Riemannian manifolds (Variations on the formula \(a^ 2=b^ 2+c^ 2-2bc\,\cos \,\alpha)).\quad\). (French) Zbl 0615.53028
Élie Cartan et les mathématiques d’aujourd’hui, The mathematical heritage of Elie Cartan, Semin. Lyon 1984, Astérisque, No.Hors Sér. 1985, 9-66 (1985).
[For the entire collection see Zbl 0573.00010.]
This is a survey article on Riemannian geometry. The important notions of the metric theory of Riemannian manifolds are explained. The discussion leads us to the newest developments in Riemannian geometry.
Reviewer: W.Ballmann
MSC:
53C20 Global Riemannian geometry, including pinching
53-02 Research exposition (monographs, survey articles) pertaining to differential geometry