Comprehensive study of intersection curves in R4 based on the system of ODEs

摘要

We propose a new approach for the study of intersection curves cI in R4 to obtain a general method for determining the Frenet frame {t,n,b1,b2} and curvatures κ1,κ2,κ3 of cI. Our method is based on the theory of differential equations, which distinguishes it from the classical methods used in previous works [4], [5], [6] that were based mainly on differential geometry. Moreover, our method is suitable for any form of hypersurface that defines the intersection curves in R4.