Lines of curvature on quadric hypersurfaces of ℝ4

详细

We describe the geometric structures of the lines of principal curvature and the partially umbilic singularities of the three-dimensional non compact generic quadric hypersurfaces of R⁴. This includes the ellipsoidal hyperboloids of one and two sheets and the toroidal hyperboloids. The present study complements the analysis of the compact ellipsoidal hypersurfaces carried out in [9].