Bertrand Curves in Minkowski Spacetime: A New Approach

Source abstract

In this study, we establish the existence conditions of non-null Bertrand curve pairs in Minkowski spacetime that preserve the classical definition of Bertrand curves, namely curve pairs with parallel principal normal vectors, where both the curves and their Frenet vectors are non-null. The corresponding Bertrand mate curves are explicitly constructed. All obtainedresults are examined with respect to every possible causal character of the curves and their Frenet vectors. Furthermore, the existence of Combescure-related curves, which form a subclass of Bertrand curves, is demonstrated as a consequence of the results. A number of examples are presented to demonstrate the theoretical results.