3 papers
math.DG2004
Shadows and convexity of surfaces
Mohammad Ghomi
We study the geometry and topology of immersed surfaces in Euclidean 3-space whose Gauss map satisfies a certain two-piece-property, and solve the ``shadow problem" formulated by H…
math.DG2003
Totally skew embeddings of manifolds
M. Ghomi, S. Tabachnikov
We obtain bounds on the least dimension of an affine space that can contain an -dimensional submanifold without any pairs of parallel or intersecting tangent lines at distinct p…
math.DG2002
Skew loops and quadric surfaces
Mohammad Ghomi, Bruce Solomon
A skew loop is a closed curve without parallel tangent lines. We prove: The only complete surfaces in euclidean 3-space with a point of positive curvature and no skew loops are the…