Riemannian Manifolds : An Introduction to Curvature (Graduate Texts in Mathematics Vol.176)

Focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. This title covers: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet's Theorem, and more.