Conformal deformation of spacelike surfaces in Minkowski space
Differential Geometry
2010-08-03 v1
Abstract
We address the problem of second order conformal deformation of spacelike surfaces in compactified Minkowski 4-space. We explain the construction of the exterior differential system of conformal deformations and discuss its general and singular solutions. In particular, we show that isothermic surfaces are singular solutions of the system, which implies that a generic second order deformable surface is not isothermic. This differs from the situation in 3-dimensional conformal geometry, where isothermic surfaces coincide with deformable surfaces.
Cite
@article{arxiv.0712.0807,
title = {Conformal deformation of spacelike surfaces in Minkowski space},
author = {Emilio Musso and Lorenzo Nicolodi},
journal= {arXiv preprint arXiv:0712.0807},
year = {2010}
}
Comments
18 pages, final version to appear in Houston J. Math.