Related papers: Regular Foliations and Poisson Structures on Orien…

In this work, we find an equation that relates the Ricci curvature of a riemannian manifold $M$ and the second fundamental forms of two orthogonal foliations of complementary dimensions, $\mathcal{F}$ and $\mathcal{F}^{\bot}$, defined on…

Given a (singular, codimension 1) holomorphic foliation F on a complex projective manifold X, we study the group PsAut(X, F) of pseudo-automorphisms of X which preserve F ; more precisely, we seek sufficient conditions for a finite index…

We give a new characterization of generalized K\"ahler structures in terms of their corresponding complex Dirac structures. We then give an alternative proof of Hitchin's partial unobstructedness for holomorphic Poisson structures. Our main…

We consider the existence of symplectic and conformal symplectic codimension-one foliations on closed manifolds of dimension at least 5. Our main theorem, based on a recent result by Bertelson-Meigniez, states that in dimension at least 7…

It is a well-known and elementary fact that a holomorphic function on a compact complex manifold without boundary is necessarily constant. The purpose of the present article is to investigate whether, or to what extent, a similar property…

We study surfaces with one constant principal curvature in Riemannian and Lorentzian three-dimensional space forms. Away from umbilic points they are characterized as one-parameter foliations by curves of constant curvature, each of these…

We introduce a notion of a weak Poisson structure on a manifold $M$ modeled on a locally convex space. This is done by specifying a Poisson bracket on a subalgebra $\cA \subeq C^\infty(M)$ which has to satisfy a non-degeneracy condition…

We summarize the foliation approach to ${\cal N}=1$ compactifications of eleven-dimensional supergravity on eight-manifolds $M$ down to $\mathrm{AdS}_3$ spaces for the case when the internal part $\xi$ of the supersymmetry generator is…

In an earlier paper, we studied manifolds $M$ endowed with a generalized F structure $\Phi\in End(TM\oplus T^*M)$, skew-symmetric with respect to the pairing metric, such that $\Phi^3+\Phi=0$. Furthermore, if $\Phi$ is integrable (in some…

Configuration spaces of many real mechanical systems appear to be manifolds with singularity. A singularity often indicates that geometry of motion may change at the singular point of configuration space. We face conceptual problem…

We investigate some genuine Poisson geometric objects in the modular theory of an arbitrary von Neumann algebra $\mathfrak{M}$. Specifically, for any standard form realization $(\mathfrak{M},\mathcal{H},J,\mathcal{P})$, we find a canonical…

We investigate the geometric, algebraic and homologic structures related with Poisson structure on a smooth manifold. Introduce a noncommutative foundations of these structures for a Poisson algebra. Introduce and investigate noncommutative…

We introduce a new class of Poisson structures on a Riemannian manifold. A Poisson structure in this class will be called a Killing-Poisson structure. The class of Killing-Poisson structures contains the class of symplectic structures, the…

Let $M$ be a closed orientable irreducible $3$-manifold such that $\pi_1(M)$ is left orderable. (a) Let $M_0 = M - Int(B^{3})$, where $B^{3}$ is a compact $3$-ball in $M$. We have a process to produce a co-orientable Reebless foliation…

Some positive answers to the problem of endowing a dynamical system with a Hamiltonian formulation are presented within the class of Poisson structures in a geometric framework. We address this problem on orientable manifolds and by using…

It is well known that a foliation F of a smooth manifold M gives rise to a rich cohomological theory, its characteristic (i.e., leafwise) cohomology. Characteristic cohomologies of F may be interpreted, to some extent, as functions on the…

Let $(M, \mathcal{F})$ be a compact Riemannian foliated manifold. We consider a family of compatible Feller semigroups in $C(M^n)$ associated to laws of the $n$-point motion. Under some assumptions (Le Jan and Raimond, \cite{Le…

We prove that a submanifold with parallel focal structure, which is a generalization of isoparametric and equifocal submanifolds, induces a singular Riemannian foliation of the ambient space by its parallel and focal manifolds.

The Poisson structures for 3D systems possessing one constant of motion can always be constructed from the solution of a linear PDE. When two constants of the motion are available the problem reduces to a quadrature and the structure…

We establish existence of functorial orbifold reductions of singularities for Poisson subvarieties in smooth Poisson threefolds. Namely, we show that with enough weighted blowups, one can reduce the singularities of such Poisson…