We revisit the Lagrange and Delaunay systems of equations of celestial mechanics, and point out a previously neglected aspect of these equations: in both cases the orbit resides on a certain 9(N-1)-dimensional submanifold of the 12(N-1)-dimensional space spanned by the orbital elements and their time derivatives. We demonstrate that there exists a vast freedom in choosing this submanifold. This...

We revisit the Lagrange and Delaunay systems of equations for the orbital elements, and point out a previously neglected aspect of these equations: in both cases the orbit resides on a certain 9-dimensional submanifold of the 12-dimensional space spanned by the orbital elements and their time derivatives. We demonstrate that there exists a vast freedom in choosing this submanifold. This freedom...

A contact stationary Legendrian submanifold of S is a Legendrian submanifold whose volume is stationary under contact deformations. The simplest contact stationary Legendrian submanifold (actually minimal and Legendrian) is the real, equatorial n-sphere S0. This paper develops a method for constructing contact stationary (but not minimal) Legendrian submanifolds of S by gluing together configur...

We solve the generalized Milnor–Hirzebruch problem on the relations between Chern numbers of an arbitrary stably almost complex manifold and Chern numbers of its virtual Chern submanifolds. As a corollary we derive new divisibility conditions for Chern classes of an arbitrary complex vector bundle over a stably almost complex manifold. Introduction The generalized Milnor–Hirzebruch problem was ...

The exceptional Dehn filling conjecture of the second author concerning the relationship between exceptional slopes α, β on the boundary of a hyperbolic knot manifold M has been verified in all cases other than small Seifert filling slopes. In this paper we verify it when α is a small Seifert filling slope and β is a toroidal filling slope in the generic case where M admits no punctured-torus f...