1. If the geodesic flow of a metric G on the torus T 2 is quadratically integrable then the torus T 2 isometrically covers a torus with a Liouville metric on it. 2. The set of quadratically integrable geodesic flows on the Klein bottle is described. §

We give explicit deformations of embeddings of abstractly planar graphs that lie on the standard torus T 2 ⊂ R3 and that contain neither a nontrivial knot nor a nonsplit link into the plane. It follows that ravels do not embed on the torus. Our results provide general insight into properties of molecules that are synthesized on a torus.

D0-brane theory on a torus with a nonvanishing B field is embedded into a string theory in the weak coupling limit. It is shown that the usual supersymmetric Yang-Mills theory on a noncommutative torus can not be the whole story. The Born-Infeld action survives the noncommutative torus limit.

Abstra t. In this paper, we onsider the hamiltonian properties of two-dimensional torus networks with the set F of faulty elements(verti es and/or edges). We will show that (1) if m 3, n 3, and n is odd, m n torus F is hamiltonianonne ted for any F with jF j 1, (2) if both m and n with m;n 4, are even, m n torus F is bihamiltonianonne ted for any F with jF j 1, and (3) if m 3, n 3, and n is odd...

In this paper we investigate the problem of how to schedule n independent jobs on an m m torus based network. We develop a model to to quantify the effect of contention for communication links on the dilation of job execution time when multiple jobs share communication links; we then design an efficient algorithm to schedule a set of n independent jobs with different torus size requirements on ...

We show that the image cone of a moment map for an action of a torus on a contact compact connected manifold is a convex polyhedral cone and that the moment map has connected fibers provided the dimension of the torus is bigger than 2 and that no orbit is tangent to the contact distribution. This may be considered as a version of the Atiyah Guillemin Sternberg convexity theorem for torus action...

We propose a new autonomous dynamical system of dimension N = 4 that demonstrates the regime of stable two-frequency motions and period-doubling bifurcations of a two-dimensional torus. It is shown that the period-doubling bifurcation of the two-dimensional torus is not followed by the resonance phenomenon, and the two-dimensional ergodic torus undergoes a period-doubling bifurcation. The inter...

The magnetic energy and inductance of current distributions on the surface of a torus are considered. Specifically, we investigate the influence of the aspect ratio of the torus, and of the pitch angle for helical current densities, on the energy. We show that, for a fixed surface area of the torus, the energy experiences a minimum for a certain pitch angle. New analytical relationships are pre...

Several conditions are given when a packing of equal discs in a torus is locally maximally dense, where the torus is defined as the quotient of the plane by a two-dimensional lattice. Conjectures are presented that claim that the density of any collectively jammed packing, whose graph does not consist of all triangles, and the torus lattice is the standard triangular lattice, is at most (n/(n +...

We prove that any asymptotically locally Euclidean scalar-flat Kähler 4-orbifold whose isometry group contains a 2-torus is isometric, up to an orbifold covering, to a quaternionic-complex quotient of a k-dimensional quaternionic vector space by a (k − 1)-torus. In order to do so, we first prove that any compact anti-self-dual 4-orbifold with positive Euler characteristic whose isometry group c...