Search

We prove the nonexistence of a nontrivial integral that is a polynomial in momenta of degree ≤ 6 for the Zipoy-Voorhees spacetime with the parameter &dgr;= 2. [ABSTRACT FROM AUTHOR]

If a closed manifold M possesses two Riemannian metrics which have the same unparameterized geodesics and are not strictly proportional at each point, then the topological entropy of both geodesic flows is zero. This is the main result of the paper and it has many dynamical and topological corollaries. In particular, such a manifold M should be finitely covered by the product of a rationally elliptic manifold and a torus.

Abstract.:  In this paper we prove that only pseudoholomorphic curves appear as J-invariant submanifolds of generic almost complex manifolds (M,J). We also prove there exist no non-trivial automorphisms or submersions of such manifolds. On the other hand we show that abundance of 1-jets of PH-submanifolds, automorphisms or submersions implies integrability of the almost complex structure.