A smooth curve on the plane can have a tangent which touches it tangentially at any number of points (Fig. 56), but this is not true for generic curves. By a small perturbation of the curve one can always achieve that no straight line will be tangential at more than two points.
Unable to display preview. Download preview PDF.
- O. A. Platonova’s Thesis (in Russian). Moscow State University, 1981, 150 p.).Google Scholar
- E. E. Landis’s Thesis (in Russian). Moscow State University, 1983, 142 p.).Google Scholar
- V. I. Arnol’d: Singularities of systems of rays. Usp. Mat. Nauk 38:2 (1983), 77–147 (English translation: Russ. Math. Surv. 38:2 (1983), 87-176).Google Scholar
- O. P. Shcherbak: Projectively dual space curves and Legendre singularities (in Russian). Tr. Tbilis. Univ. 232-233, ser. Mat. Mekh. Astron. 13-14 (1982), 280–336.Google Scholar
The proofs of the theorems on the projections depend on :
- V. I. Arnol’d: Indices of singular points of 1-forms on a manifold with boundary, convolution of invariants of reflection groups, and singular projections of smooth surfaces. Usp. Mat. Nauk 34:2 (1979), 3–38 (English translation: Russ. Math. Surv. 34:2 (1979), 1-42).Google Scholar
- T. Banchoff, T. Gaffney, C. McCrory: Cusps of Gauss mappings. Res. Notes Math. 55, Pitman, Boston-London-Melbourne 1982.Google Scholar