Close Curves In Euclidean Space And Minkowski Space

In Euclidean space,a smooth space curve whose position vector always lie in the orthogonal complement of its first binormal vector field is called a osculating curve.In Minkowski space E14,a smooth space curve whose position vector always lie in the orthogonal complement of its first binormal vector field is called the second kind osculating curve.In this thesis,we describe the osculating curves in Euclidean space and the second kind osculating curves in Minkowski space E14.In the third chapter,we first give the necessary and sufficient conditions of that a smooth space curve is a osculating curve on certain conditions.And then we focus on osculating curves whose first curvature k1(s)is nonzero constant,at the same time we get the necessary and sufficient conditions of that a space curve whose first curvature is nonzero constant is a osculating curve,next we determined the equation of the osculating curve.Finally,we also describe osculating curves in n-dimensional Euclidean space En.In the fourth chapter,we mainly study the second kind osculating curves in Minkows-ki space E14.Firstly,we give the necessary and sufficient condition of that a space curve in Minkowski space E14 is the second kind osculating curve.And then we give the clas-sification of the second kind osculating curves whose first curvature K1(s)is nonzero constant in Minkowski space E14.