Geodesics and Global Geometry
DOI link for Geodesics and Global Geometry
Geodesics and Global Geometry book
Our streamlined approach has avoided a deep study of geodesics or even the exponential map. This chapter discusses geodesics and some theorems that draw global conclusions from local curvature hypotheses. For example, Bonnet's Theorem 9.5 obtains a bound on the diameter of M from a bound on the sectional curvature. Cheeger and Ebin [Chel] and Petersen [Petl, Pet2] provide beautiful references on such topics in global Riemannian Geometry.