Generalized Bertrand and Mannheim Curves in 3D Lie Groups

INEXTENSIBLE FLOWS OF CURVES IN LIE GROUPS

In this paper, we study inextensible ows in three dimensional Lie groups with a bi-invariant metric. The necessary and sucient conditions for inextensible curve ow are expressed as a partial dierential equation involving the curvatures. Also, we give some results for special cases of Lie groups.

geometrical categories of generalized lie groups and lie group-groupoids

in this paper we construct the category of coverings of fundamental generalized lie group-groupoid associatedwith a connected generalized lie group. we show that this category is equivalent to the category of coverings of aconnected generalized lie group. in addition, we prove the category of coverings of generalized lie groupgroupoidand the category of actions of this generalized lie group-gro...

Generalized Timelike Mannheim Curves in Minkowski Space - Time E 41

Extremal Curves in Nilpotent Lie Groups

We classify extremal curves in free nilpotent Lie groups. The classification is obtained via an explicit integration of the adjoint equation in Pontryagin Maximum Principle. It turns out that abnormal extremals are precisely the horizontal curves contained in algebraic varieties of a specific type. We also extend the results to the nonfree case.

Generalized Lie Bialgebras and Jacobi Structures on Lie Groups

We study generalized Lie bialgebroids over a single point, that is, generalized Lie bialgebras. Lie bialgebras are examples of generalized Lie bialgebras. Moreover, we prove that the last ones can be considered as the infinitesimal invariants of Lie groups endowed with a certain type of Jacobi structures. We also propose a method to obtain generalized Lie bialgebras. It is a generalization of t...