Geodesics and almost geodesics curves (Q1635084)

An \textit{almost geodesic} of an affine connection \(\nabla\) on a manifold is a curve \(x(t)\) in the manifold so that \[ \nabla^2_{\dot{x}}\dot{x}=a\nabla_{\dot{x}} \dot{x}+b\dot{x}, \] for some real-valued continuous functions \(a(t)\), \(b(t)\). A curve in Euclidean space is \textit{warm} if it is almost geodesic for some constant coefficient affine connection, \textit{hot} if its image is warm under any translation or rescaling of variables. The authors determine the hot curves in Euclidean space.