A Symplectic Integrator for Riemannian Manifolds
نویسندگان
چکیده
The connguration spaces of mechanical systems usually support Riemannian metrics which have a explicitly solvable geodesic ows and parallel transport operators. While not of primary interest, such metrics can be used to generate integration algorithms by using the known parallel transport to evolve points in velocity phase space.
منابع مشابه
Nonlinear Sigma Models and Symplectic Geometry on Loop Spaces of (Pseudo)Riemannian Manifolds
In this paper we consider symplectic and Hamiltonian structures of systems generated by actions of sigma-model type and show that these systems are naturally connected with specific symplectic geometry on loop spaces of Riemannian and pseudoRiemannian manifolds. † On leave of absence from VNIIFTRI, Mendeleevo, Moscow Region 141570, Russia 1
متن کاملA Convergence Theorem for Riemannian Submanifolds
In this paper we study the convergence of Riemannian submanifolds. In particular, we prove that any sequence of closed submanifolds with bounded normal curvature and volume in a closed Riemannian manifold subconverge to a closed submanifold in the C1 ,Q topology. We also obtain some applications to irreducible homogeneous manifolds and pseudo-holomorphic curves in symplectic manifolds.
متن کاملPrehomogeneous Affine Representations and Flat Pseudo-Riemannian Manifolds
The theory of flat Pseudo-Riemannian manifolds and flat affine manifolds is closely connected to the topic of prehomogeneous affine representations of Lie groups. In this article, we exhibit several aspects of this correspondence. At the heart of our presentation is a development of the theory of characteristic classes and characters of prehomogeneous affine representations. We give application...
متن کاملKilling-Poisson tensors on Riemannian manifolds
We introduce a new class of Poisson structures on a Riemannian manifold. A Poisson structure in this class will be called a Killing-Poisson structure. The class of Killing-Poisson structures contains the class of symplectic structures, the class of Poisson structures studied in (Differential Geometry and its Applications, Vol. 20, Issue 3 (2004), 279–291) and the class of Poisson structures ind...
متن کاملHyperkähler Geometry and the Moduli Space of Higgs Bundles
Today will be mostly preliminaries, including some complex and symplectic geometry, such as the symplectic quotient, and an introduction to Kähler and hyperkähler geometry. Over the rest of the week, we’ll discuss some examples (which are usually left implicit) such as quiver varieties, introduce the moduli space of Higgs bundles, and more. A good reference for this is Andy Neitzke’s lecture no...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1996