Related papers: On low-dimensional manifolds with isometric $\math…

We prove that if a compact, simply connected Riemannian $G$-manifold $M$ has orbit space $M/G$ isometric to some other quotient $N/H$ with $N$ having zero topological entropy, then $M$ is rationally elliptic. This result, which generalizes…

Let $G$ be a unimodular Lie group, $X$ a compact manifold with boundary, and $M$ be the total space of a principal bundle $G\to M\to X$ so that $M$ is also a strongly pseudoconvex complex manifold. In this work, we show that if $G$ acts by…

In this paper, we study a class of generalized intersection matrix Lie algebras $\gim(M_n)$, and prove that its every finite-dimensional semi-simple quotient is of type $M(n,{\bf a}, {\bf c},{\bf d})$. Particularly, any finite dimensional…

We prove that SL(n,Q) has no nontrivial, C-infinity, volume-preserving action on any compact manifold of dimension strictly less than n. More generally, suppose G is a connected, isotropic, almost-simple algebraic group over Q, such that…

Let $G$ be a Lie group $G$ with representation $\rho$ on a real simple $G$-module $\mathbb{V}$. We will call the orbits of the induced action of $\rho$ on the projectivization $P\mathbb{V}$ the projective orbits, and projective orbits of…

In this paper, we assume that all isoparametric submanifolds have flat section. The main purpose of this paper is to prove that, if a full irreducible complete isoparametric submanifold of codimension greater than one in a symmetric space…

Given a faithful finite-dimensional representation $V$ of a finite group $G$ over any field $\mathbb{F}$, we show that any irreducible ${\mathbb{F}}G$-module $W$ appears, as a submodule or a quotient, in $\mathrm{Sym}^m(V)$ for some integer…

We define the notion of action of an L-infinity algebra $g$ on a graded manifold $M$, and show that such an action corresponds to a homological vector field on $g[1] \times M$ of a specific form. This generalizes the correspondence between…

Let $(M,g)$ be a non-compact riemannian $n$-manifold with bounded geometry at order $k\geq\frac{n}{2}$. We show that if the spectrum of the Laplacian starts with $q+1$ discrete eigenvalues isolated from the essential spectrum, and if the…

Sixty years ago, S. B. Myers and N. E. Steenrod ({\it Ann. of Math.} {\bf 40} (1939), 400-416) showed that the isometry group of a Riemannian manifold without boundary has a structure of Lie group. Recently A. V. Bagaev and N. I. Zhukova…

Let $G$ be an anisotropic semisimple group over a totally real number field $F$. Suppose that $G$ is compact at all but one infinite place $v_0$. In addition, suppose that $G_{v_0}$ is $\mathbb{R}$-almost simple, not split, and has a Cartan…

We present some classification results for quasitoric manifolds (M) with (p_1(M)=-\sum a_i^2) for some (a_i\in H^2(M)) which admit an action of a compact connected Lie-group (G) such that (\dim M/G \leq 1). In contrast to Kuroki's work we…

Let $(M,g^{TM})$ be an odd dimensional ($\dim M\geq 3$) connected oriented noncompact complete spin Riemannian manifold. Let $k^{TM}$ be the associated scalar curvature. Let $f:M\to S^{\dim M}(1)$ be a smooth area decreasing map which is…

We study conformal actions of connected nilpotent Lie groups on compact pseudo-Riemannian manifolds. We prove that if a type-(p,q) compact manifold M supports a conformal action of a connected nilpotent group H, then the degree of…

Let $G$ be a compact Lie group. We introduce a semiclassical framework, called Borel-Weil calculus, to investigate $G$-equivariant (pseudo)differential operators acting on $G$-principal bundles over closed manifolds. In this calculus, the…

The article is devoted to the question whether the orbit space of a compact linear group is a topological manifold and a homological manifold. In the paper, the case of a simple three-dimensional group is considered. An upper bound is…

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…

In this paper, we recall some general properties and theorems about Translating Solitons in Semi Riemannian Manifolds. Moreover, we investigate those which are invariant by the action of a Lie group of isometries of the ambient space, by…

An isometric compact group action $G \times (M,g) \rightarrow (M,g)$ is called polar if there exists a closed embedded submanifold $\Sigma \subseteq M$ which meets all orbits orthogonally. Let $\Pi$ be the associated generalized Weyl group.…

In the main theorem of this paper we treat the problem of existence of minimizers of the isoperimetric problem under the assumption of small volumes. Applications of the main theorem to asymptotic expansions of the isoperimetric problem are…