2002/05/21 by Mohammad Ghomi, Ghomi, Mohammad, Bruce Solomon +1
Mathematics · #53A04 (Primary) 53A05 #53A15 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53A04 #msc:53A05 #msc:53A15
paper · pdf · doi:10.48550/arxiv.math/0205222
14 pages, no figures; 11/02 revision corrects a small error in the original manuscript
arxiv created 2002/11/12 · arxiv updated 2009/11/30
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 quadrics. In particular, ellipsoids are the only closed surfaces without skew loops. We also prove results about skew loops on cylinders and positively curved surfaces.