On the geometry of Hamiltonian vector fields

Abstract

It is known that vector fields play an important role in many areas of mathematics and technology, in particular, in the theory of dynamical systems. Hamiltonian dynamical systems are generated by Hamiltonian vector fields. The paper studies the geometry of a singular foliation of a four-dimensional Euclidean space generated by the orbits of two Hamiltonian vector fields. It is proved that the regular leaf of this foliation is a surface of positive normal curvature and nonzero normal torsion.