|Location:||MSRI: Simons Auditorium|
The Jacobi-Maupertuis principle converts natural mechanical systems at fixed
energy into geodesic flow of a certain metric. We will find some sectional curvatures of
the metric associated to the four body problem with a 1/r2 potential (forces proportional
to the inverse distances cubed) and equal masses. Then we will deduce some dynamical
consequences for the collinear, parallelogram, or trapezoidal four body subproblems.