Framed Curves In Hyperbolic 3-Space

In this thesis,we investigate a special kind of curve,namely framed curves,in hyperbolic 3-space.A framed curve in hyperbolic 3-space is a smooth curve with a moving frame.Typical examples offramed curves are regular curves.Therefore,in some sense,the framed curve is a natural generalisation of’the regular curve.In chapter one,we prepare some basic notions on Minkowski 4-space and give the definition of hyperbolic 3-space as a kind of pseudo sphere in Minkowski space.In chapter two,the definition of framed curves in hyperbolic 3-space will be firstly introduced.Moreover,we give the Frenet-Serret type formula and curvature functions for the framed curve.Furthermore,we also show three examples of the framed curves.In chapter three,we examine the properties of the framed curves.As results,we consider the contact between framed curves,and orthogonal projections of framed curves along the normal direction.