Muñoz Masqué, JaimePozo Coronado, Luis Miguel2023-06-202023-06-2019990266-561110.1088/0266-5611/15/4/303https://hdl.handle.net/20.500.14352/57771The notion of unrolling of a spherical curve is proved to coincide with its development into the tangent plane. The development of a curve in an arbitrary surface in the Euclidean 3-space is then studied from the point of view of unrolling. The inverse operation, called the rolling of a curve onto a surface, is also analysed and the relationship of such notions with the functional defined by the square of curvature is stated. An application to the construction of nonlinear splines on Riemannian surfaces is suggested.engjournal articlehttp://iopscience.iop.org/0266-5611/15/4/303/pdf/0266-5611_15_4_303.pdfhttp://iopscience.iop.orgrestricted access514RollingunrollingLevi-Civita connectionSpline interpolationGeometría1204 Geometría