We study the geometry of compact Lorentzian manifolds that admit a somewhere timelike Killing vector field, and whose isometry group has infinitely many connected components. Up to a finite cover, such manifolds are products (or amalgamated products) of a flat Lorentzian torus and a compact Riemannian (resp., lightlike) manifold.

Let f : M ! E m be an immersion of a manifold in a Euclidean space. called the cubic representation of the submanifold. The purpose of this article is to investigate the geometry of the cubic representation of a spherical submanifold. Several theorems in this respect are obtained.

Abstract We describe a method, based on contact topology, of showing the existence semi-infinite trajectories Hamiltonian flows which start one Legendrian submanifold and asymptotically converge to another submanifold. discuss mathematical model non-equilibrium thermodynamics where such play role relaxation processes, illustrate our results in case Glauber dynamics for mean field Ising model.

Let 800(1, n) denote the connected component of the group of linear transformations of IRn+l preserving the bilinear form Abstract Using techniques of Lie groups and ergodic theory, it can be shown that in a compact manifold of constant negative curvature, the closure of a totally geodesic, complete (immersed) submanifold of dimension atleast 2 is a totally geodesicimmersed submanifold. The mai...

We propose a method to analyze infrared contributions to non-inclusive processes in QCD. We use the one-loop Sudakov form factor as a working example. Borrowing techniques from renormalization theory, we construct coun-terterms for the contributions from the soft and collinear regions, and we relate them to eikonal Wilson lines taken along non-lightlike directions.

Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper, we study the geometry of a semi-Riemannian manifold ¯ M of quasi-constant curvature. The main result is two characterization theorems for ¯ M admits solenoidal and screen totally umbilical r (> 1)-lightlike subm...

We give some estimates of the first eigenvalue of the Laplacian for compact and non-compact submanifold immersed in the Euclidean space by using the square length of the second fundamental form of the submanifold merely. Then some spherical theorems and a nonimmersibility theorem of Chern and Kuiper type can be obtained.

Given a Lagrangian submanifold in a symplectic manifold and a Morse function on the submanifold, we show that there is an isotopic Morse function and a symplectic Lefschetz pencil on the manifold extending the Morse function to the whole manifold. From this construction we define a sequence of symplectic invariants classifying the isotopy classes of Lagrangian spheres in a symplectic 4-manifold.

In [19], we proved that, under certain hypotheses, the moduli space of an asymptotically cylindrical special Lagrangian submanifold with fixed boundary of an asymptotically cylindrical Calabi-Yau 3-fold is a smooth manifold. Here we prove the analogous result for an asymptotically cylindrical special Lagrangian submanifold with moving boundary.