A variational principle for actions on symmetric symplectic spaces

We present a definition of generating functions of canonical relations, which are real functions on symmetric symplectic spaces, discussing some conditions for the presence of caustics. We show how the actions compose by a neat geometrical formula and are connected to the hamiltonians via a geometrically simple variational principle which determines the classical trajectories, discussing the temporal evolution of such ``extended hamiltonians'' in terms of Hamilton-Jacobi-type equations. Simplest spaces are treated explicitly.Comment: 28 pages. Edited english translation of first author's PhD thesis (2000

Harmonic Maps with Prescribed Singularities on Unbounded Domains

The Einstein/Abelian-Yang-Mills Equations reduce in the stationary and axially symmetric case to a harmonic map with prescribed singularities \p\colon\R^3\sm\Sigma\to\H^{k+1}_\C into the $(k+1)$-dimensional complex hyperbolic space. In this paper, we prove the existence and uniqueness of harmonic maps with prescribed singularities \p\colon\R^n\sm\Sigma\to\H, where $\Sigma$ is an unbounded smooth closed submanifold of $\R^n$ of codimension at least $2$, and \H is a real, complex, or quaternionic hyperbolic space. As a corollary, we prove the existence of solutions to the reduced stationary and axially symmetric Einstein/Abelian-Yang-Mills Equations.Comment: LaTeX2e (amsart) with packages: amssymb, euscript, xspace, 11 page