English

Skew loops in flat tori

Differential Geometry 2007-07-01 v3

Abstract

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.

Keywords

Cite

@article{arxiv.math/0701913,
  title  = {Skew loops in flat tori},
  author = {Bruce Solomon},
  journal= {arXiv preprint arXiv:math/0701913},
  year   = {2007}
}