Topology of Surfaces with Connected Shades

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.

Keywords

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.

Full Text (PDF format)

Published 1 January 2007