Asian Journal of Mathematics
Volume 11 (2007)
Topology of Surfaces with Connected Shades
Pages: 621 – 634
We prove that any closed orientable surface may be smoothly embedded in Euclidean 3-space so that when it is illuminated by parallel rays from any direction the shade cast on the surface is connected.
Shadow; shade; vision number; skew loop; tantrix; constant mean curvature; gauss map; two-piece-property; tight immersion
2010 Mathematics Subject Classification
Primary 53A04, 53A05. Secondary 52A15, 53C42.