Kinematic geometry of triangles and the study of the three-body problem.
Let and be graded Lie algebras whose grading is in or , but only one of them. Suppose that is a derivatively knitted pair of representations for , i.e. and satisfy equations which look “derivatively knitted"; then , endowed with a suitable bracket, which mimics semidirect products on both sides, becomes a graded Lie algebra . This graded Lie algebra is called the knit product of and . The author investigates the general situation for any graded Lie subalgebras and of a graded...
We realize closed geodesics on the real conformal compactification of the space V = Sym(2, ℝ) of all 2 × 2 real symmetric matrices as knots or 2-component links in and show that these knots or links have certain types of symmetry of period 2.