This paper develops a method for generating tra-jectories for a rigid body with speciied boundary conditions at the end points and intermediate locations. It is well known that SE(3), the set of all rigid body positions and orientations, is a non Euclidean space. In general, the problem of determining trajectories that are optimal with respect to some meaningful metric does not have an analytic...

There is a well known one–parameter family of left invariant CR structures on SU(2) ∼= S. We show how purely algebraic methods can be used to explicitly compute the canonical Cartan connections associated to these structures and their curvatures. We also obtain explicit descriptions of tractor bundles and tractor connections.

Ray Singer torsion is a numerical invariant associated with a compact manifold equipped with a flat bundle, a Riemannian metric on the manifold and a Hermitian structure on the bundle. In this note we show how one can remove the dependence on the Riemannian metric and the Hermitian structure with the help of a base point and of an Euler structure, and obtain a topological invariant. A numerical...

The Camassa-Holm (CH) and Hunter-Saxton (HS) equations have an interpretation as geodesic flow equations on the group of diffeomorphisms, preserving the H and Ḣ right-invariant metrics correspondingly. There is an analogy to the Euler equations in hydrodynamics, which describe geodesic flow for a right-invariant metric on the infinitedimensional group of diffeomorphisms preserving the volume el...