On Joachimsthal’s theorems in semi-Euclidean spaces

In this work, we study Joachimsthal’s theorems in semi-Euclidean spaces Eνn+1. We obtain a relation between the curvatures of the strips in semi-Euclidean spaces Eνn+1 in matrix form depending on a semi-orthogonal matrix. This matrix equation gives us a generalization of the original Joachimsthal theorem in semi-Euclidean space E13 and the well-known Joachimsthal theorem of the surface theory. In addition, we reobtain the well-known Joachimsthal theorem from our matrix equation in the case n=2,ν=0n=2,ν=0 and the original Joachimsthal theorem from our matrix equation in the case n=2,ν=1n=2,ν=1.