Perturbations of curvatures flow in a hyperbolic space

摘要

A representation of a special type of the variational problem on a surface immersed in a hyperbolic space is given. The perturbations of the mean curvature functional are studied. For this study, the corresponding frames are constructed and the polar surfaces of a given surface is established. The technique adapted here is based on Cartan’s methods of moving frames, exterior differential forms and the group of motions [Result. Math. 39 (2001) 1; Tensor. N.S. 51 (3) (1992) 224; Tensor. N.S. 59 (1998) 36; Collect. Math., universtat de Barcelona 45 (1994) 153].