# Geodesic distance

From Encyclopedia of Mathematics

The length of the shortest geodesic line connecting two points (or two sets). In variational calculus the geodesic distance is the extremal value of the functional under study concerning extremals connecting the two points.

#### Comments

#### References

[a1] | H. Busemann, "The geometry of geodesics" , Acad. Press (1955) |

[a2] | W. Klingenberg, "Riemannian geometry" , de Gruyter (1982) (Translated from German) |

**How to Cite This Entry:**

Geodesic distance.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Geodesic_distance&oldid=17325