Related papers: Isometric Lie 2-group actions on Riemannian groupo…

For each left-invariant Riemannian metric on simply connected nonunimodular Lie groups of dimension four, we determine the full group of isometries.

We characterize the universal covering of connected analytic pseudo-Riemannian manifolds which admit a non-trivial and isometric action of the simple Lie group $SL(3,\mathbb{R})$ with a dense orbit preserving a finite volume. If such…

For each left-invariant semi-Riemannian metric $g$ on a Lie group $G$, we introduce the class of bi-Lipschitz Riemannian Clairaut metrics, whose completeness implies the completeness of $g$. When the adjoint representation of $G$ satisfies…

We complete the construction of the double Lie algebroid of a double Lie groupoid begun in the first paper of this title. We show that the Lie algebroid structure of an LA--groupoid may be prolonged to the Lie algebroid of its Lie groupoid…

We study the relationship between multiplicative 2-forms on Lie groupoids and linear 2-forms on Lie algebroids, which leads to a new approach to the infinitesimal description of multiplicative 2-forms and to the integration of twisted Dirac…

For a strict Lie 2-group, we develop a notion of Lie 2-algebra-valued differential forms on Lie groupoids, furnishing a differential graded-commutative Lie algebra equipped with an adjoint action of the Lie 2-group and a pullback operation…

We establish rigidity for partial transformation groupoids associated with algebraic actions of semigroups: If two such groupoids (satisfying appropriate conditions) are isomorphic, then the globalizations of the initial algebraic actions…

We study tensors on Lie groupoids suitably compatible with the groupoid structure, called {\em multiplicative}. Our main result gives a complete description of these objects only in terms of infinitesimal data. Special cases include the…

It is shown that the problem of reduction can be formulated in a uniform way using the theory of invariants. This provides a powerful tool of analysis and it opens the road to new applications of these algebras, beyond the context of…

We study left-invariant pseudo-Riemannian metrics on Lie groups using the bracket flow of the corresponding Lie algebra. We focus on metrics where the Lie algebra is in the null cone of the $G=O(p,q)$-action; i.e., Lie algebras $\mu$ where…

Symplectic slice theorems elucidate the local structure of symplectic manifolds carrying Hamiltonian actions of compact Lie groups. We generalize these theorems in two natural settings. The first is based on the idea that complex reductive…

We show the contractibility of spaces of invariant Riemannian metrics of positive scalar curvature on compact connected manifolds of dimension at least two, with and without boundary and equipped with compact Lie group actions. On manifolds…

We derive sharp estimates comparing asymptotic Riemannian or sub-Riemannian metrics in 2-step nilpotent Lie groups. For each metric, we construct a Carnot metric whose square remains at bounded distance from the square of the original…

In this short note we provide an elementary proof of the folklore result in the theory of isometric Lie group actions on Riemannian manifolds asserting that sections of polar actions are totally geodesic.

We prove a 2-categorical analogue of a classical result of Drinfeld: there is a one-to-one correspondence between connected, simply-connected Poisson Lie 2-groups and Lie 2-bialgebras. In fact, we also prove that there is a one-to-one…

We study isometric Lie group actions on symmetric spaces admitting a section, i.e. a submanifold which meets all orbits orthogonally at every intersection point. We classify such actions on the compact symmetric spaces with simple isometry…

A Riemann-Lie algebra is a Lie algebra $\cal G$ such that its dual ${\cal G}^*$ carries a Riemannian metric compatible (in the sense introduced by th author in C. R. Acad. Paris, t. 333, S\'erie I, (2001) 763-768) with the canonical linear…

This paper is a continuations of the project initiated in the book string topology for stacks. We construct string operations on the SO(2)-equivariant homology of the (free) loop space $L(X)$ of an oriented differentiable stack $X$ and show…

Associated to any manifold equipped with a closed form of degree >1 is an `L-infinity algebra of observables' which acts as a higher/homotopy analog of the Poisson algebra of functions on a symplectic manifold. In order to study Lie group…

In this work we deal with coverings and actions of Lie group- groupoids being a sort of the structured Lie groupoids. Firstly, we define an action of a Lie group-groupoid on some Lie group and the smooth coverings of Lie group-groupoids.…