ARIZONA STATE UNIVERSITY Interpolation in Lie Groups and Homogeneous Spaces
نویسنده
چکیده
We consider interpolation in Lie groups and homogeneous spaces. Based on points on the manifold together with tangent vectors at (some of) these points, we construct Hermite interpolation polynomials. If the points and tangent vectors are produced in the process of integrating an ordinary di erential equation on a Lie group or a homogeneous space, we use the truncated inverse of the di erential of the exponential mapping and the truncated BakerCampbell-Hausdor formula to relatively cheaply construct an interpolation polynomial. Much e ort has lately been put into research on geometric integration, i.e. the process of integrating a di erential equation in such a way that the con guration space is respected by the numerical solution. Some of these methods may be viewed as generalizations of classical methods, and we investigate the construction of intrinsic dense output devices as generalizations of the continuous Runge-Kutta methods. AMS Subject Classi cation: 65L06, 34A50
منابع مشابه
Short talks
This talk concerns Dirichlet and Neumann boundary value problems for second order elliptic divergence form equations with non-symmetric, or more general complex, and measurable coefficients independent of the transversal coordinate in the upper half space. I shall discuss some recent results obtained which shows that, in the case of non-symmetric coefficients, the solutions obtained with the bo...
متن کاملHomogeneous symplectic manifolds of Poisson-Lie groups
Symplectic manifolds which are homogeneous spaces of Poisson-Lie groups are studied in this paper. We show that these spaces are, under certain assumptions, covering spaces of dressing orbits of the Poisson-Lie groups which act on them. The effect of the Poisson induction procedure on such spaces is also examined, thus leading to an interesting generalization of the notion of homogeneous space....
متن کاملOrbit Spaces Arising from Isometric Actions on Hyperbolic Spaces
Let be a differentiable action of a Lie group on a differentiable manifold and consider the orbit space with the quotient topology. Dimension of is called the cohomogeneity of the action of on . If is a differentiable manifold of cohomogeneity one under the action of a compact and connected Lie group, then the orbit space is homeomorphic to one of the spaces , , or . In this paper we suppo...
متن کاملSampling and Interpolation on Some Nilpotent Lie Groups
Let N be a non-commutative, simply connected, connected, two-step nilpotent Lie group with Lie algebra n such that n = a⊕ b⊕ z, [a, b] ⊆ z, the algebras a, b, z are abelian, a = R-span {X1, X2, · · · , Xd} , and b = R-span {Y1, Y2, · · · , Yd} . Also, we assume that det [[Xi, Yj ]]1≤i,j≤d is a non-vanishing homogeneous polynomial in the unknowns Z1, · · · , Zn−2d where {Z1, · · · , Zn−2d} is a ...
متن کاملCurvature homogeneous spaces whose curvature tensors have large symmetries
We study curvature homogeneous spaces or locally homogeneous spaces whose curvature tensors are invariant by the action of “large” Lie subalgebras h of so(n). In this paper we deal with the cases of h = so(r)⊕ so(n− r) (2 ≤ r ≤ n− r), so(n− 2), and the Lie algebras of Lie groups acting transitively on spheres, and classify such curvature homogeneous spaces or locally homogeneous spaces.
متن کامل