Spacelike Framed Curves with Lightlike Components and Singularities of Their Evolutes and Focal Surfaces in Minkowski 3-space

In this paper,we define the evolute and focal surface of a spacelike framed curve with lightlike components in Minkowski 3-space.It is a generalization of the previous results of regular spacelike curves,since singularities are allowed in the original spacelike curves studied by spacelike framed curves with lightlike components.Meanwhile,we show a new geometric invariant to characterise singularities of the focal surface.Then,the classification theorem and recognition theorem for the singularities of the focal surface in generic are also given.