A curve that locally minimizes the distance between two points on any mathematically defined space, such as a curved manifold. Equivalently, it is a path of minimal curvature. In noncurved three-dimensional space, the geodesic is a straight line. In General Relativity, the trajectory of a body with negligible mass on which only gravitational forces are acting (i.e. a free falling body) is a geodesic in (curved) 4-dimensional space-time.

Adjective

Of or relating to the branch of geometry that deals with geodesics.