Related papers: Adapted complex tubes on the symplectization of ps…

We establish a relation between the growth of the cylindrical contact homology of a contact manifold and the topological entropy of Reeb flows on this manifold. We show that if a contact manifold $(M,\xi)$ admits a hypertight contact form…

We study the approximation of functions that map a Euclidean domain $\Omega\subset \mathbb{R}^{d}$ into an $n$-dimensional Riemannian manifold $(M,g)$ minimizing an elliptic, semilinear energy in a function set $H\subset W^{1,2}(\Omega,M)$.…

For every CR-manifold germ (M,a) local tube realizations are characterized by certain abelian subalgebras of the real Lie algebra hol(M,a) of all germs of (real-analytic) infinitesimal transformations. For instance, if M is holomorphically…

We construct a locally geometric $\infty$-stack $M_{Hod}(X,Perf)$ of perfect complexes with $\lambda$-connection structure on a smooth projective variety $X$. This maps to $A ^1 / G_m$, so it can be considered as the Hodge filtration of its…

In this paper we look at the question of integrability, or not, of the two natural almost complex structures $J^{\pm}_\nabla$ defined on the twistor space $J(M,g)$ of an even-dimensional manifold $M$ with additional structures $g$ and…

Let $\Gamma$ be a minimal connected negative-definite plumbing tree with all vertices of genus zero, and let $Y_\Gamma$ be the oriented link of the corresponding normal complex surface singularity, equipped with its canonical contact…

We introduce a canonical affine connection on the contact manifold $(Q,\xi)$, which is associated to each contact triad $(Q,\lambda,J)$ where $\lambda$ is a contact form and $J:\xi \to \xi$ is an endomorphism with $J^2 = -id$ compatible to…

Let $(M,g)$ be a pseudo-Riemannian manifold and $F_\lambda(M)$ the space of densities of degree $\lambda$ on $M$. We study the space $D^2_{\lambda,\mu}(M)$ of second-order differential operators from $F_\lambda(M)$ to $F_\mu(M)$. If $(M,g)$…

A-manifolds and A-bundles are manifolds and vector bundles modelled on a projective finitely generated module over a topological algebra A. In this paper we investigate the conditions under which an A-bundle is provided with an A-valued…

The spaces of Riemannian metrics on a closed manifold $M$ are studied. On the space ${\mathcal M}$ of all Riemannian metrics on $M$ the various weak Riemannian structures are defined and the corresponding connections are studied. The space…

We give necessary conditions for certain real analytic tube generic submanifolds in C^n to be locally algebraizable. As an application, we exhibit families of real analytic non locally algebraizable tube generic submanifolds in C^n. During…

Let $X$ be a compact complex manifold which admits a hermitian metric satisfying a curvature condition introduced by Guan-Li. Given a semipositive form $\theta$ with positive volume, we define the Monge-Amp\`ere operator for unbounded…

The class of the hypercomplex pseudo-Hermitian manifolds is considered. The flatness of the considered manifolds with the 3 parallel complex structures is proved. Conformal transformations of the metrics are introduced. The conformal…

We show that the manifold $(\mathbb{S}^2 \times \mathbb{S}^2) \operatorname{\#} (\mathbb{S}^2 \times \mathbb{S}^2)$ does not admit a non-constant non-injective uniformly quasiregular self-map. This answers a question of Martin, Mayer, and…

Let $M$ be a pseudo-Hermitian homogeneous space of finite volume. We show that $M$ is compact and the identity component $G$ of the group of holomorphic isometries of $M$ is compact. If $M$ is simply connected, then even the full group of…

Let $(M,\omega)$ be a symplectic manifold endowed with a agrangian foliation ${\cal L}$, it has been shown by Weinstein [16] hat the symplectic structure of $M$ defines on each leaf of ${\cal L}$, connection which curvature and torsion…

Let $\psi:\M \to \SH$ be an isometric immersion of codimension 1, then there exist symmetric $(1,1)$-tensors $S$ and $f$, a tangent vector field $U$ and a smooth function $\lambda$ on $\M$ that satisfy the compatibility equations of $\SH$.…

On a compact symplectic manifold $(X,\omega)$ with a prequantum line bundle $(L,\nabla,h)$, we consider the one-parameter family of $\omega$-compatible complex structures which converges to the real polarization coming from the Lagrangian…

We develop a method for describing invariant Monge-Amp\`ere equations in the sense of V. Lychagin and T. Morimoto (MAE) on a homogeneous contact manifold $N$ of a semisimple Lie group $G$, which is the contactification of the homogeneous…

Let $S^*Q$ be the spherization of a closed connected manifold of dimension at least two. Consider a contactomorphism $\varphi$ that can be reached by a contact isotopy that is everywhere positively transverse to the contact structure. In…