Rectifying Curves in 4-D Minkowski Space

The flat four-dimensional spacetime of relativity, called Minkowski space, distinguishes vectors into three categories: space-like, light-like, and time-like. One way of analyzing smooth, regular curves in this space is through use of the orthonormal Frenet-frame, which assigns a basis for each point along the curve. The four unit vector functions are called the tangent, normal, first binormal, and second binormal. A rectifying curve is a linear combination of the tangent and two binormal vectors. In this presentation I will give the necessary and sufficient conditions for when a time-like curve in Minkowski space is rectifying.