Asian Journal of Mathematics

Volume 11 (2007)

Number 4

Topology of Surfaces with Connected Shades

Pages: 621 – 634

DOI: http://dx.doi.org/10.4310/AJM.2007.v11.n4.a5

Author

Mohammad Ghomi

Abstract

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.

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