Riemannian geometry (Q5917594)

In the third edition of this very interesting textbook the authors mainly added a new section (in chapter 2) devoted to pseudo-Riemannian geometry. There are presented space-like, time-like and light-like curves, the Minkowski space, the de Sitter spaces, some results concerning the completeness in pseudo-Riemannian geometry (Marsden's theorem, Carrière's theorem), the Schwarzschild metric. They also added an introduction to isosystolic inequalities, were Loewner's theorem is presented as well as some comments concerning this theory, a description of the geodesic flow from the Hamiltonian point of view, the equality case for the Bishop-Gromov inequality.