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Automorphisms of spatial curves

Ivan Bradáč (1997)

Archivum Mathematicum

Automorphisms of curves y = y ( x ) , z = z ( x ) in 𝐑 3 are investigated; i.e. invertible transformations, where the coordinates of the transformed curve y ¯ = y ¯ ( x ¯ ) , z ¯ = z ¯ ( x ¯ ) depend on the derivatives of the original one up to some finite order m . While in the two-dimensional space the problem is completely resolved (the only possible transformations are the well-known contact transformations), the three-dimensional case proves to be much more complicated. Therefore, results (in the form of some systems of partial differential equations...

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