In mathematics, a geoesic /ˌdʒiəˈdɛsɪk, -ˈdisɪk/[jee-uh-des-ik, -dee-sik] is a generalization of the notion of a "straight line" to "curved spaces". In presence of a metric, geodesics are defined to be (locally) the shortest path between points on the space. In the presence of an affine connection, geodesics are defined to be curves whose tangent vectors remain parallel if they are transported along it.