Special Curves And Developable Surfaces In 3-Space Minkowski

The relavant papers of S.Izumiya has mainly studied the three dimensional Euclidean space curves and the singularity classification of developable surfaces ,Minkowski geometry has provided the theoretical model in mathematics for Einstein's relativity theory . Especially, four dimensional Minkowski space has the very strong physical background. As the sub- space of four dimensional Minkowski space , The three dimensional Minkowski space have many properties which are different from three-dimensional Euclidean space,because it has three kind of different vectors,and has the lightcone especially. Therefore we study special curve and developable surfaces' properties as well as the relations of special curve and developable surfaces, , We give singularity classification of the three dimensional Minkowski space's developable surfaces . There will has the very important practical significance,also. In Dong he Pei Professor related papers, the spacelike curve and timelike curve of three-dimensional Minkowski space is given , and give the singularity classification of three-dimensional Minkowski space, developable surfaces which is relevant to these two type of curves. however,there have been no papers which have investigated Minkowski and Minkowski slant helices and Minkowski conical geodesic curves so far as.In this paper,our major study is to give the definition of Minkowski general helix and Minkowski slant helices and Minkowski conical geodesic curves in indicators 1 in pseudo-Euclidean three-space (that is, three-dimensional Minkowski space), and study the definition of equivalence Minkowski general helix, By considering geometric invariants of these space curves, we can estimate the order of contact with those special curves for general space curves.By the definition of Darboux type vector and rectifying Darboux type vector ,we constructed the rectifying type developable surfaces and Darboux type developable surfaces and tangential Darboux type developable surfaces ,and study these three developable surfaces' relationship with Minkowski slant helices and Minkowski conical geodesic curves. Bying applying the singularity theoerical knowledge, We give a classification of special developable surfaces under the condition of the existence of such a special curve as geodesic.