Related papers: Tangent bundles to sub-Riemannian groups

We explicitly determine the group of isomorphism classes of equivariant line bundles on the non-archimedean Drinfeld upper half plane for $\mathrm{GL}_2(F)$, for its subgroups of matrices whose determinant has even (respectively trivial)…

For a connected Lie group G, we show that a complex structure on the total space TG of the tangent bundle of G that is left invariant and has the property that each left translation G-orbit is a totally real submanifold is induced from a…

We study the structure of Lie groups admitting left invariant abelian complex structures in terms of commutative associative algebras. If, in addition, the Lie group is equipped with a left invariant Hermitian structure, it turns out that…

This work is a spin-off of an on-going programme which aims at revisiting the original studies of Lie and Cartan on pseudogroups and geometric structures from a modern perspective. We encode geometric structures induced by transitive Lie…

We introduce the concept of Hypoelliptic Diffusion Maps (HDM), a framework generalizing Diffusion Maps in the context of manifold learning and dimensionality reduction. Standard non-linear dimensionality reduction methods (e.g., LLE,…

Let $X$ be a differentiable manifold endowed with a transitive action $\alpha:A\times X\longrightarrow X$ of a Lie group $A$. Let $K$ be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms…

The aim of the paper is to popularise nilpotent Lie groups (notably the Heisenberg group and alike) in the context of Clifford analysis and related models of mathematical physics. It is argued that these groups are underinvestigated in…

We show that a connected, simply connected nilpotent Lie group with an integrable left-invariant complex structure on a generating and suitably complemented subbundle of the tangent bundle admits a CR embedding in complex space as the edge…

A result from Gromov ensures the existence of a contact structure on any connected non-compact odd dimensional Lie group. But in general such structures are not invariant under left translations of the Lie group. The problem of finding…

Symmetric connections that are compatible with semi-Riemannian metrics can be characterized using an existence result for an integral leaf of a (possibly non integrable) distribution. In this paper we give necessary and sufficient…

The existence of a recurrent spinor field on a pseudo-Riemannian spin manifold $(M,g)$ is closely related to the existence of a parallel 1-dimensional complex subbundle of the spinor bundle of $(M,g)$. We characterize the following simply…

In this paper, we investigate left invariant Riemannian metrics on Lie groups with one and two-dimensional commutator subgroups. We explicitly provide the Levi-Civita connection, sectional curvature, and Ricci curvature, and we give…

In this paper we construct infinitely many examples of a Riemannian submersion from a simple, compact Lie group $G$ with bi-invariant metric onto a smooth manifold that cannot be a quotient of $G$ by a group action. This partially addresses…

The article presents a bundle framework for nonlinear observer design on a manifold with a Lie group action. The group action on the manifold decomposes the manifold to a quotient structure and an orbit space, and the problem of observer…

It is shown that for any compact Lie group $G$ (odd or even dimensional), the tangent bundle $TG$ admits a left-invariant integrable almost complex structure, where the Lie group structure on $TG$ is the natural one induced from $G$. The…

We define a subcategory of the category of diffeological spaces, which contains smooth manifolds, the diffeomorphism subgroups and its coadjoint orbits. In these spaces we construct a tangent bundle, vector fields and a de Rham cohomology.

Let G be compact Lie group. It is shown that the cotangent bundle of the complexification of G admits a hyperkahler structure which is invariant under left and right translations by elements of G. The proof is to realize the cotangent…

In this work, generalized principal bundles modelled by Lie group bundle actions are investigated. In particular, the definition of equivariant connections in these bundles, associated to Lie group bundle connections, is provided, together…

A relative Picard theory in the context of graded manifolds is introduced. A Berezinian calculus and a theory of connections over SUSY-curves are systematically developed, and used to prove a Gauss-Bonnet theorem for line bundles in that…

We are interested in the classification of left-invariant symplectic structures on Lie groups. Some classifications are known, especially in low dimensions. In this paper we establish a new approach to classify (up to automorphism and…