Geodesics of nonholonomic left-invariant intrinsic metrics on the Heisenberg group and isoperimetric curves on the Minkowski plane
Let \(H\) be the Heisenberg group of real upper-triangular \((3 \times 3)\)- matrices with unity entries in the principal diagonal and let \(d_c\) be an arbitrary nonholonomic metric on \(H\). Among other things the author proves that a curve in \((H,d_c)\) starting at the unity \(e \in H\) is a geodesic if and only if it satisfies Pontryagin's maximum principle for an associated time-optimal control problem.
scientific article; zbMATH DE number 794611