FAMILIES OF SURFACES IN ℝ4

We study the geometry of surfaces in $\mathbb{R}^4$ associated to contact with hyperplanes. We list all possible transitions that occur on the parabolic and so-called $A_3$-set, and analyse the configurations of the asymptotic curves and their bifurcations in generic one-parameter families.AMS 2000 Mathematics subject classification: Primary 58C27. Secondary 53A05