Related papers: Contact projective structures and chains

Cosymplectic and normal almost contact structures are analogues of symplectic and complex structures that can be defined on 3-manifolds. Their existence imposes strong topological constraints. Generalized geometry offers a natural common…

Nous montrons que les seules vari\'et\'es toriques munies d'une structure de contact sont, \`a isomorphisme pr\`es, les espaces projectifs complexes et les vari\'et\'es $\mathbb{P}_{\mathbb{P}^{1}\times\cdots\times\mathbb{P}^{1}}…

We give necessary and sufficient geometric conditions for a distribution (or a Pfaffian system) to be locally equivalent to the canonical contact system on Jn(R,Rm), the space of n-jets of maps from R into Rm. We study the geometry of that…

A general model for geometric structures on differentiable manifolds is obtained by deforming infinitesimal symmetries. Specifically, this model consists of a Lie algebroid, equipped with an affine connection compatible with the Lie…

We describe the automorphisms of a singular multicontact structure, that is a generalisation of the Martinet distribution. Such a structure is interpreted as a para-CR structure on a hypersurface M of a direct product space R^2 x R^2. We…

We study contact structures on nonnegatively-graded manifolds equipped with homological contact vector fields. In the degree 1 case, we show that there is a one-to-one correspondence between such structures (with fixed contact form) and…

In the literature different concepts of compatibility between a projective structure and a conformal structure on a differentiable manifold are used. In particular compatibility in the sense of Weyl geometry is slightly more general than…

This paper introduces a new class of geometric structures in almost contact metric geometry, which we call locally conformal almost generalized $f$-cosymplectic manifolds. These are almost contact metric structures $(\phi, \xi, \eta, g)$…

Almost hypercomplex manifolds with Hermitian and anti-Hermitian metrics are considered. A linear connection $D$ is introduced such that the structure of these manifolds is parallel with respect to D. Of special interest is the class of the…

In this note we study the connection between the existence of a projective reconstruction and the existence of a fundamental matrix satisfying the epipolar constraints.

Complex contact manifolds arise naturally in differential geometry, algebraic geometry and exterior differential systems. Their classification would answer an important question about holonomy groups. The geometry of such manifold $X$ is…

We consider normal almost contact structures on a Riemannian manifold and, through their associated sections of an ad-hoc twistor bundle, study their harmonicity, as sections or as maps. We rewrite these harmonicity equations in terms of…

We prove the connectedness and calculate the diameter of the oriented graph of graftings associated to exotic complex projective structures on a compact surface S with a given holonomy representation of Fuchsian type. The oriented graph of…

For a semisimple Lie group $G$ with parabolic subgroups $Q\subset P\subset G$, we associate to a parabolic geometry of type $(G,P)$ on a smooth manifold $N$ the correspondence space $\Cal CN$, which is the total space of a fiber bundle over…

We consider smooth deformations of the $CR$ structure of a smooth $2$-pseudoconcave compact $CR$ submanifold $\textsf{M}$ of a reduced complex analytic variety $\textsf{X}$ outside the intersection $D\,{\cap}\,\textsf{M}$ with the support…

The present note deals with the dynamics of metric connections with vectorial torsion, as already described by E. Cartan in 1925. We show that the geodesics of metric connections with vectorial torsion defined by gradient vector fields…

We give a notion of compatibility between a Riemannian structure and a Jacobi structure. We prove that in case of fundamental examples of Jacobi structures : Poisson structures, contact structures and locally conformally symplectic…

We characterise the integrability of any co-CR quaternionic structure in terms of the curvature and a generalized torsion of the connection. Also, we apply this result to obtain, for example, the following. (1) New co-CR quaternionic…

We consider a pair of smooth manifolds, which are the counterparts in the even-dimensional and odd-dimensional cases. They are separately an almost complex manifold with Norden metric and an almost contact manifolds with B-metric,…

1-flat irreducible G-structures, equivalently, irreducible G-structures admitting torsion-free affine connections, have been studied extensively in differential geometry, especially in connection with the theory of affine holonomy groups.…