ABSTRACT
D A geodesic e is a curve such that its tangent vector field X is autopara//el along c: (8-51)
In local coordinates, this geodesic equation is written under the form of the n following differential equations:
dJ(' +r' X j X k = 0 dt Jk
or
(8-52)
Let us find again the geodesic equations from calculus of variations which consists in obtaining exlremal curves (basic calculus ofvariations!). In this context, the geodesic distance between two points of an open set U is the lower bound (if it exists) of curve lengths joining the points and lying in U. The geodesic arc is the arc corresponding to this lower bound.
