Geodesic
In differential geometry, a geodesic (/ˌdʒiːəˈdɛsɪk, ˌdʒiːoʊ-, -ˈdiː-, -zɪk/) is a generalization of the notion of a "straight line" to "curved spaces".
Description
In the presence of an affine connection, a geodesic is defined to be a curve whose tangent vectors remain parallel if they are transported along it.
If this connection is the Levi-Civita connection induced by a Riemannian metric, then the geodesics are (locally) the shortest path between points in the space.
Terminology
The term "geodesic" comes from geodesy, the science of measuring the size and shape of Earth; in the original sense, a geodesic was the shortest route between two points on the Earth's surface, namely, a segment of a great circle.
The term has been generalized to include measurements in much more general mathematical spaces; for example, in graph theory, one might consider a geodesic between two vertices/nodes of a graph.
General relativity
Geodesics are of particular importance in general relativity. Timelike geodesics in general relativity describe the motion of inertial test particles.
See also
External links
- Geodesic @ Wikipedia
