Surfaces in $\mathbb{R}^4$ and their projections to 3-spaces

Real and Complex Singularities

In this paper a Minkowski analogue of the Euclidean medial axis of a closed and smooth plane curve is introduced. Its generic local configurations are studied and the types of shocks that occur on these are also determined.

ASYMPTOTIC CURVES ON SURFACES IN ℝ5

We study asymptotic curves on generically immersed surfaces in ℝ5. We characterize asymptotic directions via the contact of the surface with flat objects (k-planes, k = 1 - 4), give the equation of the asymptotic curves in terms of the coefficients of the second fundamental form and study their generic local configurations.