Some Relations Between Normal and Rectifying Curves in Minkowski Space-Time

Abstract

In this paper, we firstly give the necessary and sufficient conditions for null, pseudo null and partially null curves in Minkowski space-time to be normal curves. We prove that the null, pseudo null and partially null normal curves have a common property that their orthogonal projection onto non-degenerate hyperplane of E 4 1 or onto lightlike 2-plane of E 4 1 is the corresponding rectifying curve. Finally, we give some examples of such curves in E 4 1 .

On generalized null Mannheim curves in Minkowski space-time

“…Recall that a normal curve in E 4 1 is defined in [8] as a curve the position vector of which always lies in its normal space T ⊥ , which represents the orthogonal complement of the tangent vector field T of the curve.…”

Some Null Quaternionic Curves in Minkowski spaces

“…A Bertrand curve is a curve which has common principal normal vectors with another curve and characterized by speciality that Rectifying curves were defined by Chen in 2003 [3]. At the same year, İlarslan et al studied rectifying curves in Minkowski 3-space [11]. Then, more mathematicians studied about rectifying curves in some spaces [2-4, 9, 15].…”

Classification of Rectifying Space-Like Submanifolds in Pseudo-Euclidean Spaces

“…Rectifying curves have many interesting properties. Such curves have been studied by many authors, see for instance, [1,3,10,9,13,14,15] among many others.…”