Some Geometric Invariants of Pseudo-Spherical Evolutes in the Hyperbolic 3-Space

In this paper,we study the pseudo-spherical evolutes of curves in three dimensional hyperbolic space.We use techniques from singularity theory to investigate the singularities of pseudo-spherical evolutes and establish some relationships between singularities of these curves and geometric invariants of curves under the action of the Lorentz group.Besides,we defray with illustration some computational examples in support our main results.

Hamiltonian Structure, Soliton Solution and Conservation Laws for a New Fifth-Order Nonlinear Evolution Equation Which Describes Pseudo-Spherical Surfaces

In this paper, we shall show that the Hamiltonian structure can be defined for any nonlinear evolution equations which describe surfaces of a constant negative curvature, so that the densities of conservation laws can be considered as corresponding Hamiltonians. This paper obtains the soliton solution and conserved quantities of a new fifth-order nonlinear evolution equation by the aid of inverse scattering method.