Linear connections for systems of second-order ordinary differential equations
Linear connections on almost commutative algebras.
Linear direct connections
In this paper we study the geometry of direct connections in smooth vector bundles (see N. Teleman [Tn.3]); we show that the infinitesimal part, , of a direct connection τ is a linear connection. We determine the curvature tensor of the associated linear connection As an application of these results, we present a direct proof of N. Teleman’s Theorem 6.2 [Tn.3], which shows that it is possible to represent the Chern character of smooth vector bundles as the periodic cyclic homology class of a...
Linear Growth Harmonic Functions on Complete Manifolds with Nonnegative Ricci Curvature.
Linear hamiltonian circle actions that generate minimal Hilbert bases
The orbit space of a linear Hamiltonian circle action and the reduced orbit space, at zero, are examples of singular Poisson spaces. The orbit space inherits the Poisson algebra of functions invariant under the linear circle action and the reduced orbit space inherits the Poisson algebra obtained by restricting the invariant functions to the reduced space. Both spaces reside inside smooth manifolds, which in turn inherit almost Poisson structures from the Poisson varieties. In this paper we consider...
Linear liftings of affinors to Weil bundles
We give a classification of all linear natural operators transforming affinors on each n-dimensional manifold M into affinors on , where is the product preserving bundle functor given by a Weil algebra A, under the condition that n ≥ 2.
Linear liftings of skew-symmetric tensor fields to Weil bundles
We define equivariant tensors for every non-negative integer and every Weil algebra and establish a one-to-one correspondence between the equivariant tensors and linear natural operators lifting skew-symmetric tensor fields of type on an -dimensional manifold to tensor fields of type on if . Moreover, we determine explicitly the equivariant tensors for the Weil algebras , where and are non-negative integers.
Linear transformations of -connections in . II.
Lineare invariante Gebilde in äquiformen Bewegungen der Räume endlicher Dimension
Linearization and explicit solutions of the minimal surface equations.
We show that the apparatus of support functions, usually used in convex surfaces theory, leads to the linear equation Δh + 2h = 0 describing locally germs of minimal surfaces. Here Δ is the Laplace-Beltrami operator on the standard two-dimensional sphere. It explains the existence of the sum operator of minimal surfaces, introduced recently. In 4-dimensional space the equation Δ h + 2h = 0 becomes inequality wherever the Gauss curvature of a minimal hypersurface is nonzero.
Linearization and star products
The aim of this paper is to give an overview concerning the problem of linearization of Poisson structures, more precisely we give results concerning Poisson-Lie groups and we apply those cohomological techniques to star products.
Linearization of Poisson actions and singular values of matrix products
We prove that the linearization functor from the category of Hamiltonian -actions with group-valued moment maps in the sense of Lu, to the category of ordinary Hamiltonian - actions, preserves products up to symplectic isomorphism. As an application, we give a new proof of the Thompson conjecture on singular values of matrix products and extend this result to the case of real matrices. We give a formula for the Liouville volume of these spaces and obtain from it a hyperbolic version of the Duflo...
L'inégalité de Penrose
Lines of curvature, ridges and conformal invariants of hypersurfaces.
Lines vortices in the U(1) - Higgs model
For a given U(1)-bundle E over M = {x1, ..., xn}, where the xi are n distinct points of , we minimise the U(1)-Higgs action and we make an asymptotic analysis of the minimizers when the coupling constant tends to infinity. We prove that the curvature (= magnetic field) converges to a limiting curvature that we give explicitely and which is singular along line vortices which connect the xi. This work is the three dimensional equivalent of previous works in dimension two (see [3] and [4]). The...
Linien, Flächen und höhere Gebilde in mehrfach ausgedehnten Gausschen und Riemannschen Räumen
Linked Darboux motions.
Linking and the Morse complex
For a Morse function on a compact oriented manifold , we show that has more critical points than the number required by the Morse inequalities if and only if there exists a certain class of link in whose components have nontrivial linking number, such that the minimal value of on one of the components is larger than its maximal value on the other. Indeed we characterize the precise number of critical points of in terms of the Betti numbers of and the behavior of with respect to links....
Liouville forms in a neighborhood of an isotropic embedding
A Liouville form on a symplectic manifold is by definition a potential of the symplectic form . Its center is given by . A normal form for certain Liouville forms in a neighborhood of its center is given.
Liouville theorem for harmonic maps with potential.