Isoperimetric extremals of rotation functionals on two-dimensional connected Lie groups with invariant Riemannian metrics (Q1603057)

In two-dimensional connected Lie groups \(M^2\) endowed with a Riemannian metric \(g\), the isoperimetric rotation extremals (abbreviated, the IREs) are determined whose family consists of the geodesics of the manifold \((M^2,g)\) and of the curves \(\gamma\) which satisfy the equation \(K=\hat{c}\cdot k\), where \(K\) is the curvature of \(g\) on \(\gamma\), \(\hat{c}\) is an isoperimetric constant depending on the length of \(\gamma\) and \(k\) is the curvature of \(\gamma\).