Geometric conditions for the existence of an intrinsic rolling

摘要: We give a complete answer to the question of when two curves in different Riemannian manifolds can be seen as trajectories rolling one manifold on other without twisting or slipping. show that up technical hypotheses, along these exists if and only geodesic curvatures each curve coincide. By using anti-developments curves, which we claim generalization curvatures, are able extend result arbitrary absolutely continuous curves. For constant sectional curvature itself, such differ by an isometry. In case surfaces, conditions for loops lift configuration space rolling.