A generalization of Lancret's theorem

General helices in a three dimensional Lie group with a bi-invariant metric are defined and a generalization of Lancret's theorem is obtained. We conclude that the so-called spherical images of general helices are plane curves, and we obtain the so-called spherical general helices. We also give a relation between the geodesics of the so-called cylinders and general helices. (C) 2009 Elsevier B.V. All rights reserved