Mathematics – Differential Geometry
Scientific paper
2007-01-31
Mathematics
Differential Geometry
Scientific paper
We produce skew loops -- loops having no pair of parallel tangent lines --
homotopic to any loop in a flat torus or other quotient of R^n. The interesting
case here is n=3. More subtly for any n, we characterize the homotopy classes
that will contain a skew loop having a specified loop in the unit sphere as
tangent indicatrix.
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