- #1
Pencilvester
- 184
- 42
In general, is the number of distinct geodesics between two fixed points purely a feature of the topology of the manifold? i.e. Can there ever exist two topologically equivalent (I can’t remember the proper word right now- is homeomorphic the right one?) manifolds, ##\mathcal M## and ##\mathcal N##, related by a bijective mapping, ##\phi : \mathcal M \to \mathcal N##, in which there exists a pair of points in ##\mathcal M##, ##\mathbf a## and ##\mathbf b## where the number of geodesics between ##\mathbf a## and ##\mathbf b## differs from the number of geodesics between ##\phi (\mathbf a )## and ##\phi (\mathbf b )##?