Osculating plane preserving diffeomorphisms (Q1856589)

For immersed differentiable curves in 3-spaces the group of self-diffeomorphisms of the parameter domain preserving the osculating plane is called the osculating group. Such diffeomorphisms preserving the tangent plane (as an affine subspace) build up the tangent group. The author classifies these groups for open and closed Frenet curves with non-vanishing torsion, showing that they are trivial in the essential cases. Planar parts coming from vanishing torsion lead to a bigger group where the transformations mainly deal with these flat pieces of the curve.