By Peter Petersen

This quantity introduces concepts and theorems of Riemannian geometry, and opens tips to complex issues. The textual content combines the geometric elements of Riemannian geometry with analytic facets of the speculation, and studies fresh examine. The up-to-date moment variation contains a new coordinate-free formulation that's simply remembered (the Koszul formulation in disguise); an accelerated variety of coordinate calculations of connection and curvature; common fomulas for curvature on Lie teams and submersions; variational calculus built-in into the textual content, taking into account an early therapy of the sector theorem utilizing a forgotten evidence via Berger; fresh effects relating to manifolds with optimistic curvature.