Lines of Affine Principal Curvatures of Surfaces in 3-Space

In this work we study the affine principal lines on surfaces in 3-space. We consider the binary differential equation of the affine curvature lines and obtain the topological models of these curves near the affine umbilic points (elliptic and hyperbolic). We also describe the local generic behavior of affine curvature lines at points with double eigenvalues of the affine shape operator and at parabolic points.