Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1895596 | Journal of Geometry and Physics | 2014 | 11 Pages |
Abstract
We show that the solutions of the constant astigmatism equation that correspond to a class of surfaces found by Lipschitz in 1887, exactly match the Lie symmetry invariant solutions and constitute a four-dimensional manifold. The two-dimensional orbit space with respect to the Lie symmetry group is described. Our approach relies on the link between constant astigmatism surfaces and orthogonal equiareal patterns. The counterpart sine-Gordon solutions are shown to be Lie symmetry invariant as well.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Adam HlaváÄ, Michal Marvan,