Non-lightlike framed isophote curves in Minkowski 3-space

This paper gives the definition of isophote curves with singularities in Minkowski 3-space and studies their geometric properties. As a key geometric consequence of the Lambert’s cosine law, isophote curves contribute to understanding the geometric and optical characteristics of objects in Minkowski space. Based on frame curve theory, we introduce the concept of non-lightlike framed isophote curves on non-lightlike surfaces. We analyze their light vectors based on their curvature functions and investigate their relationship with non-lightlike framed slant helices. Furthermore, we study the singularities and their criterion of non-lightlike framed isophote curves.