Some Characterizations Of Quasi-normal Curves And Dual Spaclike Normal Curves

Studing curves in Minkowski space not only has the actual physical significance, as well as theoretical value in mathematical. Our resesrch discusses quasi-normal curves in Minkowski 4-space, and dual spacelike curves in dual Minkowski 3-space .First, we give the definition of the quasi-normal curves; discuss the characterizati- ons of timelike quasi-normal curves ; get the necessary and sufficient condition when the curves lie on pseudosphere; we find that timelike quasi- normal curves must lie on pseudosphere, and timelike curves in pseudosphere must be timelike quasi- normal curves. next,we discuss the features of the pseudo null curves when it is quasi-normal, and the necessary and sufficient conditions when the curves lie on pseudosphere, pseudohyperbolic space and light cone.then, discuss another spacelike curves, the principal normal vector and the first binormal vector are spacelike vector, similar, we can get the feastures and conditions. The last part of the paper is to study curves in dual Minkowski 3-space, we can get the features when dual spacelike curves is normal curves and the necessary and sufficient conditions when the curves lie on dual pseudosphere, dual pseudohyperbolic space.