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math.DG2002
Projecting (n-1)-cycles to zero on hyperplanes in R^{n+1}
Bruce Solomon
The projection of a compact oriented submanifold M^{n-1} in R^{n+1} on a hyperplane P^{n} can fail to bound any region in P. We call this ``projecting to zero.'' Example: The equat…
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…