| Popis: |
If (M, g) is a Riemannian manifold, then the concept of length makes sense for any piecewise smooth (in fact, C1) curve on M. It is then possible to define the structure of a metric space on M, where d(p, q) is the greatest lower bound of the length of all curves joining p and q. Curves on M which locally yield the shortest distance between two points are of great interest. These curves, called geodesics, play an important role and the goal of this chapter is to study some of their properties. |
