INEXTENSIBLE FLOWS OF CURVES IN LIE GROUPS

Inextensible Flows of Curves in Minkowskian Space

In this paper we investigate inextensible flow of curves in Minkowski 3-space. Necessary and sufficient conditions for an inextensible curve flow are expressed as a partial differential equation involving the curvature and torsion. Mathematics Subject Classification: 53C44; 53A04; 53A05

Inextensible flows of curves and developable surfaces

The flow of a curve or surface is said to be inextensible if, in the former case, the arclength is preserved, and in the latter case, if the intrinsic curvature is preserved. Physically, inextensible curve and surface flows are characterized by the absence of any strain energy induced from the motion. In this paper we investigate inextensible flows of curves and developable surfaces in R3. Nece...

Inextensible Flows of Spacelike, Timelike and Null Curves

In this paper,we study inextensible flows of spacelike and timelike curves in E1 and we research inextensible flows of null curves in E 3 1 Mathematics Subject Classification: 53A35, 53A04, 53A05

Nonholonomic Flows on Lie Groups

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.

Lie Algebras and Lie Brackets of Lie Groups–matrix Groups

The goal of this paper is to study Lie groups, specifically matrix groups. We will begin by introducing two examples: GLn(R) and SLn(R). Then in each section we will prove basic results about our two examples and then generalize these results to general matrix groups.