Related papers: Flat Affine Manifolds And Their Transformations
Results describing Lie ideals and maximal finite-codimensional Lie subalgebras of the Lie algebras associated with Lie algebroids with non-singular anchor maps are presented. It is also proved that every isomorphism of such Lie algebras…
Two Lie algebroids are presented that are linked to the construction of the linearizing output of an affine in the input nonlinear system. The algorithmic construction of the linearizing output proceeds inductively, and each stage has two…
Let $G$ be a compact Lie group acting effectively by isometries on a compact Riemannian manifold $M$ with nonempty fixed point set $Fix(M,G)$. We say that the action is \emph{fixed point homogeneous} if $G$ acts transitively on a normal…
Let $\Gamma$ be a finite group acting on a Lie group $G$. We consider a class of group extensions $1 \to G \to \hat{G} \to \Gamma \to 1$ defined by this action and a $2$-cocycle of $\Gamma$ with values in the centre of $G$. We establish and…
A generalized Stiefel manifold is the manifold of orthonormal frames in a vector space with a non-degenerated bilinear or hermitian form. In this article, the Isometry group of the generalized Stiefel manifolds are computed at least up to…
We study smooth rational closed embeddings of the real affine line into the real affine plane, that is algebraic rational maps from the real affine line to the real affine plane which induce smooth closed embeddings of the real euclidean…
The goal of this paper is to study the geometry of the connected unit component of the real general linear Lie group $4$ dimensional $G_0$ as a Lorentzian and flat affine manifold. As the group $G_0$ is naturally equipped with a…
In this paper we study a version of the Hermitian curvature flow (HCF). We focus on complex homogeneous manifolds equipped with induced metrics. We prove that this finite-dimensional space of metrics is invariant under the HCF and write…
Given a compact, connected Lie group $K$, we use principal $K$-bundles to construct manifolds with prescribed finite-dimensional algebraic models. Conversely, let $M$ be a compact, connected, smooth manifold which supports an almost free…
This is a summary of some of the basic facts about flat 2-orbifold groups, otherwise known as 2-dimensional crystallographic groups. We relate the geometric and topological presentations of these groups, and consider structures…
We prove the following result: Let $(M,g_0)$ be a compact manifold of dimension $n\geq 12$ with positive isotropic curvature. Then $M$ is diffeomorphic to a spherical space form, or the total space of an orbifiber bundle over $\mathbb{S}^1$…
Diffeomorphism groups $G$ of manifolds $M$ on locally $\bf F$-convex spaces over non-Archimedean fields $\bf F$ are investigated. It is shown that their structure has many differences with the diffeomorphism groups of real and complex…
In this paper we generalize classical results on Lie algebras and universal enveloping algebras of Lie algebras to Lie-Rinehart algebras. We define for any Lie-Rinehart algebra $L$ and any cocycle $f$ in $Z^2(L,B)$, a universal enveloping…
A special linear Lie group over the real number field and the quarternion field admits a projectivley flat affine connection. We show that parabolic subgroups are autoparallel submanifolds and give a criterion the induced connection is…
We investigate the finite-dimensional Lie groups whose points are separated by the continuous homomorphisms into groups of invertible elements of locally convex algebras with continuous inversion that satisfy an appropriate completeness…
A unitary representation of a, possibly infinite dimensional, Lie group $G$ is called semi-bounded if the corresponding operators $i\dd\pi(x)$ from the derived representations are uniformly bounded from above on some non-empty open subset…
An example of a finite dimensional factorizable ribbon Hopf C-algebra is given by a quotient H=u_q(g) of the quantized universal enveloping algebra U_q(g) at a root of unity q of odd degree. The mapping class group M_{g,1} of a surface of…
Consider a connected manifold of dimension at least two and the group of compactly supported diffeomorphisms that are compactly supported isotopic to the identity. This group acts $n$-transitive: Any tuple of $n$ points can be moved to any…
If a (possibly finite) compact Lie group acts effectively, locally linearly, and homologically trivially on a closed, simply-connected four-manifold with second Betti number at least three, then it must be isomorphic to a subgroup of S^1 x…
We show that bi-flat $F$-manifolds can be interpreted as natural geometrical structures encoding the almost duality for Frobenius manifolds without metric. Using this framework, we extend Dubrovin's duality between orbit spaces of Coxeter…