Asian Journal of Mathematics

Topology of Surfaces with Connected Shades

Mohammad Ghomi

Full-text: Open access

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.

Article information

Source
Asian J. Math., Volume 11, Number 4 (2007), 621-634.

Dates
First available in Project Euclid: 2 May 2008

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1209735313

Mathematical Reviews number (MathSciNet)
MR2402941

Zentralblatt MATH identifier
1141.53301

Subjects
Primary: 53A05: Surfaces in Euclidean space 53A04: Curves in Euclidean space
Secondary: 52A15: Convex sets in 3 dimensions (including convex surfaces) [See also 53A05, 53C45] 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]

Keywords
Shadow shade vision number skew loop tantrix constant mean curvature gauss map two-piece-property tight immersion

Citation

Ghomi, Mohammad. Topology of Surfaces with Connected Shades. Asian J. Math. 11 (2007), no. 4, 621--634. https://projecteuclid.org/euclid.ajm/1209735313


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