Related papers: On invariants of almost symplectic connections

This article is a contribution to the understanding of the geometry of the twistor space of a symplectic manifold. We consider the bundle $Z$ with fibre the Siegel domain Sp(2n,R)/U(n) existing over any given symplectic 2n-manifold M. Then,…

The space of the torsion (0,3)-tensors of the linear connections on almost contact manifolds with B-metric is decomposed in 15 orthogonal and invariant subspaces with respect to the action of the structure group. Three known connections,…

We study piecewise linear knot diagrams in the base of almost toric fibrations of symplectic four-manifolds. These diagrams translate to deformations of the almost toric fibration. We give several applications to symplectic topology, among…

The vector space of the tensors $\mathcal F$ of type (0,3) having the same symmetries as the covariant derivative of the fundamental form of an almost contact metric manifold is considered. A scheme of decomposition of $\mathcal F$ into…

Exterior differential forms with values in the (Kostant's) symplectic spinor bundle on a manifold with a given metaplectic structure are decomposed into invariant subspaces. Projections to these invariant subspaces of a covariant derivative…

The object of study is almost paracomplex pseudo-Riemannian manifolds with a pair of metrics associated each other by the almost paracomplex structure. A torsion-free connection and tensors with geometric interpretation are found which are…

Almost paracontact manifolds of an odd dimension having an almost paracomplex structure on the paracontact distribution are studied. The components of the fundamental (0,3)-tensor, derived by the covariant derivative of the structure…

We study the relations between the projective and the almost conformally symplectic structures on a smooth even dimensional manifold. We describe these relations by a single almost conformally symplectic connection with totally trace--free…

The space of the structure (0,3)-tensors of the covariant derivatives of the structure endomorphism and the metric on almost contact B-metric manifolds is considered. A known decomposition of this space in orthogonal and invariant subspaces…

We study 5-dimensional Riemannian manifolds that admit an almost contact metric structure. We classify these structures by their intrinsic torsion and review the literature in terms of this scheme. Moreover, we determine necessary and…

In this note we make several observations concerning symplectic fillings. In particular we show that a (strongly or weakly) semi-fillable contact structure is fillable and any filling embeds as a symplectic domain in a closed symplectic…

It is considered a differentiable manifold equipped with a pseudo-Riemannian metric and an almost contact 3-struc\-ture so that an almost contact metric structure and two almost contact B-metric structures are generated. There are…

In this paper, we describe the space of adapted connections on a metric contact manifold through the space of their torsion tensors. The torsion tensor is an element of the space of TM-valued two-forms, which splits into various subspaces.…

The class of the Riemannian almost product manifolds with nonintegrable structure is considered. Some identities for curvature tensor as certain invariant tensors and quantities are obtained.

In this paper we study finite dimensional algebras, in particular finite semifields, through their correspondence with nonsingular threefold tensors. We introduce a alternative embedding of the tensor product space into a projective space.…

We study symplectic manifolds $(M^{2l},\omega)$ equipped with a symplectic torsion-free affine (also called Fedosov) connection $\nabla$ and admitting a metaplectic structure. Let $\mathcal{S}$ be the so called symplectic spinor bundle and…

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…

We study the decomposition of the Riemannian curvature R tensor of an almost quaternion-Hermitian manifold under the action of its structure group Sp(n)Sp(1). Using the minimal connection, we show that most components are determined by the…

We investigate G-invariant symplectic structures on the cotangent bundle T*P of a principal G-bundle P(M,G) which are canonically related to automorphisms of the tangent bundle TP covering the identity map of P and commuting with the action…

We generalize Turaev's definition of torsion invariants of pairs (M,x), where M is a 3-dimensional manifold and x is an Euler structure on M (a non-singular vector field up to homotopy relative to bM and local modifications in int(M).…