Generalized helices in three-dimensional Lie groups

Authors: ALEXANDER YAMPOLSKY, ANASTASIYA OPARIY

Abstract: We introduce three types of helices in three-dimensional Lie groups with left-invariant metric and give their geometrical description similar to that of Lancret. We generalize the results known for the case of three-dimensional Lie groups with bi-invariant metric.

Keywords: Slant helix, Lancret's theorem, curves in Lie groups

Full Text: PDF