Related papers: Tangent bundles to sub-Riemannian groups

In earlier work (*) we studied an extension of the canonical symplectic structure in the cotangent bundle of an affine space ${\cal Q}={\bf R}^N$, by additional terms implying the Poisson non-commutativity of both configuration and momentum…

Given a saturated Fell bundle A over an inverse semigroup S which is semi-abelian in the sense that the fibers over the idempotents of S are commutative, we construct a twisted etale groupoid L such that A can be recovered from L in a…

Lie groups considered as three-dimensional almost paracontact almost paracomplex Riemannian manifolds are investigated. In each basic class of the classification used for the manifolds under consideration, a correspondence is established…

We propose a general procedure to construct noncommutative deformations of an embedded submanifold $M$ of $\mathbb{R}^n$ determined by a set of smooth equations $f^a(x)=0$. We use the framework of Drinfel'd twist deformation of differential…

We construct a Clifford algebra bundle formed from the tangent bundle of the smooth loop space of a Riemannian manifold, which is a bundle of super von Neumann algebras on the loop space. We show that this bundle is in general non-trivial,…

This paper presents a geometric description on Lie algebroids of Lagrangian systems subject to nonholonomic constraints. The Lie algebroid framework provides a natural generalization of classical tangent bundle geometry. We define the…

Let $(M,\nabla,\langle\;,\;\rangle)$ be a manifold endowed with a flat torsionless connection $\nabla$ and a Riemannian metric $\langle\;,\;\rangle$ and $(T^kM)_{k\geq1}$ the sequence of tangent bundles given by $T^kM=T(T^{k-1}M)$ and…

Following our approach to metric Lie algebras developed in math.DG/0312243 we propose a way of understanding pseudo-Riemannian symmetric spaces which are not semi-simple. We introduce cohomology sets (called quadratic cohomology) associated…

In this paper, we study Riemannian, anti-invariant Riemannian and Lagrangian submersions. We prove that the horizontal distribution of a Lagrangian submersion from a Kaehlerian manifold is integrable. We also give some applications of this…

We study the $\bar{\partial}$-Laplacian on forms taking values in $L^{k}$, a high power of a nef line bundle on a compact complex manifold, and give an estimate of the number of the eigenforms whose corresponding eigenvalues smaller than or…

A Riemannian manifold is called \emph{weakly Einstein} if the tensor $R_{iabc}R_{j}^{~~abc}$ is a scalar multiple of the metric tensor $g_{ij}$. We consider weakly Einstein Lie groups with a left-invariant metric which are weakly Einstein.…

We develop a complete theory of non-formal deformation quantization on the cotangent bundle of a weakly exponential Lie group. An appropriate integral formula for the star-product is introduced together with a suitable space of functions on…

Submanifold theory is a very active vast research field which plays an important role in the development of modern differential geometry. This branch of differential geometry is still so far from being exhausted; only a small portion of an…

We obtain the Plancherel theorem for the quotient of a simple Lie group of real rank one by a convex-cocompact discrete subgroup and its consequences for the spectrum of locally invariant differential operators on bundles over Kleinian…

We introduce the convex bundle method to solve convex, non-smooth optimization problems on Riemannian manifolds of bounded sectional curvature. Each step of our method is based on a model that involves the convex hull of previously…

For transcendental values of q the quantum tangent spaces of all left-covariant first order differential calculi of dimension less than four on the quantum group $\SLq 2$ are given. All such differential calculi $\Gamma $ are determined and…

The author discusses in some detail the old definitions of the curvature tensors for rigged metrized distributions on manifolds given by Schouten, Wagner, and Solov'ev. To calculate the Solov'ev sectional and Ricci curvatures for…

In this note we are concerned with the distribution of Einstein and non-Einstein nilradicals among all nilpotent Lie groups. A nilpotent Lie group is called an Einstein, resp. non-Einstein, nilradical if it is a nilpotent Lie group which…

In this paper the classification of left-invariant Riemannian metrics, up to the action of the automorphism group, on cotangent bundle of (2n+1)-dimensional Heisenberg group is presented. Also, it is proved that the complex structure on…

We consider exact Lagrangian submanifolds in cotangent bundles. Under certain additional restrictions (triviality of the fundamental group of the cotangent bundle, and of the Maslov class and second Stiefel-Whitney class of the Lagrangian…