Related papers: Nilpotent aspherical Sasakian manifolds

In this note, We proved that a compact Sasakian manifold $( M, {\xi}, {\eta}, {\Phi} , g )$ with negative transverse holomorphic sectional curvature must have has a Sasakian structure $( {\xi}, {\eta} , {\Phi} , g )$ with negative…

This self-contained paper is part of a series \cite{FF2,FF3} on actions by diffeomorphisms of infinite groups on compact manifolds. The two main results presented here are: 1) Any homomorphism of (almost any) mapping class group or…

In this article we provide evidence for a well-known conjecture which states that quasi-isometric simply-connected nilpotent Lie groups are isomorphic. We do so by constructing new examples which are rigid in the sense that whenever they…

We prove that on a compact Sasakian manifold $(M, \eta, g)$ of dimension $2n+1$, for any $0 \le p \le n$ the wedge product with $\eta \wedge (d\eta)^p$ defines an isomorphism between the spaces of harmonic forms $\Omega^{n-p}_\Delta (M)$…

The present work is devoted to compact completely solvable solvmanifolds which admit Kahlerian metrics whose Kahler forms are homogeneous. In particular, we show that such manifolds are diffeomorphic to flat tori. Our proof is based on…

We show that almost nonnegatively curved m-dimensional manifolds are, up to finite cover, nilpotent spaces in the sense of homotopy theory and have C(m)-nilpotent fundamental groups. We also show that up to a finite cover almost…

Let $(M, \omega)$ be a connected, compact symplectic manifold equipped with a Hamiltonian $G$ action, where $G$ is a connected compact Lie group. Let $\phi$ be the moment map. In \cite{L}, we proved the following result for $G=S^1$ action:…

We explore the geometry that underlies the osculating nilpotent group structures of the Heisenberg calculus. For a smooth manifold $M$ with a distribution $H\subseteq TM$ analysts use explicit (and rather complicated) coordinate formulas to…

Let X be a compact K\"ahler manifold such that the universal cover admits a compactification. We conjecture that the fundamental group is almost abelian and reduce it to a classical conjecture of Iitaka.

We build an example of a non-transitive, dynamically coherent partially hyperbolic diffeomorphism $f$ on a closed $3$-manifold with exponential growth in its fundamental group such that $f^n$ is not isotopic to the identity for all $n\neq…

We show that the nefness of the canonical bundle of compact K\"ahler threefolds is invariant under deformed symplectic diffeomorphisms.

We show that for a Lie group $G=\R^{n}\ltimes_{\phi} \R^{m}$ with a semisimple action $\phi$ which has a cocompact discrete subgroup $\Gamma$, the solvmanifold $G/\Gamma$ admits a canonical invariant formal (i.e. all products of harmonic…

We refer to the set of the orders of elements of a finite group as its spectrum and say that groups are isospectral if their spectra coincide. We prove that with the only specific exception the solvable radical of a nonsolvable finite group…

Every partially hyperbolic diffeomorphism on a 3-dimensional nilmanifold is leaf conjugate to a nilmanifold automorphism.

We prove that a nilpotent subgroup of orientation preserving $C^{1}$ diffeomorphisms of ${\mathbb S}^{2}$ has a finite orbit of cardinality at most two. We also prove that a finitely generated nilpotent subgroup of orientation preserving…

In this paper, we show that there exists a nonconstant CR holomorphic function of polynomial growth in a complete noncompact Sasakian manifold of nonnegative pseudohermitian bisectional curvature with the CR maximal volume growth property.…

In this paper we consider smooth oriented hypersurfaces in 2-step nilpotent Lie groups with a left invariant metric and derive an expression for the Laplacian of the Gauss map for such hypersurfaces in the general case and in some…

We consider expansive group actions on a compact metric space containing a special fixed point denoted by $0$, and endomorphisms of such systems whose forward trajectories are attracted toward $0$. Such endomorphisms are called…

We address the problem of computing the fundamental group of a symplectic $S^1$-manifold for non-Hamiltonian actions on compact manifolds, and for Hamiltonian actions on non-compact manifolds with a proper moment map. We generalize known…

We prove that a closed regular $(4k+1)$-Sasakian manifold $(M,h_0)$ admits a family of non-isometric metrics $h_\rho, \rho\geq 0,$ such that $\pi_1({\rm Isom}(M, h_\rho))$, the fundamental group of the isometry group, is infinite for…