1997/03/09 by Viktor L. Ginzburg, Ginzburg, Viktor L.
Mathematics · #58Exx #Differential Geometry (math.DG) #FOS: Mathematics #dg-ga #math.DG #msc:58Exx
paper · pdf · doi:10.48550/arxiv.dg-ga/9703006
AMS-LaTeX, 11 pages, substantially revised, to appear in IMRN
arxiv created 1997/06/21 · arxiv updated 2009/11/30
A smooth counterexample to the Hamiltonian Seifert conjecture for six-dimensional symplectic manifolds is found. In particular, we construct a smooth proper function on the symplectic 2n-dimensional vector space, 2n > 4, such that one of its non-singular level sets carries no periodic orbits of the Hamiltonian flow. The function can be taken to be C0-close and isotopic to a positive-definite quadratic form so that the level set in question is isotopic to an ellipsoid. This is a refinement of previously known constructions giving such functions for 2n > 6. The proof is based on a new version of a symplectic embedding theorem applied to the horocycle flow.