Suppose that is the extended complex plane (the Riemann sphere).
Suppose is a path in . The spherical length of is defined as
Let , and let be the set of all paths in from to , then the distance from to in the spherical metric is defined as
More intuitivelly this is the shortest distance to travel from to if we think of these points as being on the Riemann sphere, and we can only travel on the Riemann sphere itself (we cannot “drill” a straight line from to ).
- 1 Theodore B. Gamelin. . Springer-Verlag, New York, New York, 2001.
|Date of creation||2013-03-22 14:18:41|
|Last modified on||2013-03-22 14:18:41|
|Last modified by||jirka (4157)|