In a 2-dimensional manifold, any curve with a tangent vector that is null at each point is indeed classified as a null geodesic. This is established due to the unique properties of null directions in such manifolds, where only two null directions exist at each point. The discussion also highlights that a curve, such as the circle of contact on a torus, may not necessarily be a null geodesic unless the metric tensor is nonsingular throughout the manifold.
PREREQUISITESMathematicians, physicists, and students of differential geometry who are interested in the properties of curves and geodesics in 2-dimensional manifolds.