Related papers: New geometric structures on 3-manifolds: surgery a…

We construct a compact example of 7- dimensional manifold endowed with a weakly integrable generalized G_2-structure with respect to a closed and non trivial 3-form. Moreover, we investigate which type of SU(3)-structures on a 6-dimensional…

This paper defines a symplectic form on the infinite dimensional Fr\'echet manifold of framed curves of fixed length over a simply connected Riemannian manifold of constant curvature. The paper then considers Hamiltonian systems generated…

A real 3-manifold is a smooth 3-manifold together with an orientation preserving smooth involution, called a real structure. In this article we study open book decompositions on smooth real 3-manifolds that are compatible with the real…

This paper is a study of almost contact statistical manifolds. Especially this study is focused on almost cosymplectic statistical manifolds. We obtained basic properties of such manifolds. It is proved a characterization theorem and a…

We study a number of local and global classification problems in generalized complex geometry. In the first topic, we characterize the local structure of generalized complex manifolds by proving that a generalized complex structure near a…

The paper contains a short review of the theory of symplectic and contact manifolds and of the generalization of this theory to the case of supermanifolds. It is shown that this generalization can be used to obtain some important results in…

Biharmonic or polyharmonic curves and surfaces in 3-dimensional contact manifolds are investigated.

Piecewise Euclidean structures (identified solid Euclidean polyhedra) on topological 3-dimensional manifolds and pseudo-manifolds are constructed so that they admit pseudo-foliations, a generalized type of foliation. The construction of…

Almost contact manifolds with B-metric are considered. A special linear connection is introduced, which preserves the almost contact B-metric structure on these manifolds. This connection is investigated on some classes of the considered…

Suppose that the 3-manifold M is given by integral surgery along a link L in S^3. In the following we construct a stable map from M to the plane, whose singular set is canonically oriented. We obtain upper bounds for the minimal numbers of…

Homogeneous compatible almost complex structures on symplectic manifolds are studied, focusing on those which are special, meaning that their Chern-Ricci form is a multiple of the symplectic form. Non Chern-Ricci flat ones are proven to be…

In this paper, we give a complete topological, as well as geometrical classification of closed 3-dimensional Lorentz manifolds admitting a noncompact isometry group.

Despite spectacular advances in defining invariants for simply connected smooth and symplectic 4-dimensional manifolds and the discovery of effective surgical techniques, we still have been unable to classify simply connected smooth…

By use of a variety of techniques (most based on constructions of quasipositive knots and links, some old and others new), many smooth 3-manifolds are realized as transverse intersections of complex surfaces in complex 3-space with strictly…

Generalized complex geometry, as developed by Hitchin, contains complex and symplectic geometry as its extremal special cases. In this thesis, we explore novel phenomena exhibited by this geometry, such as the natural action of a B-field.…

A generalized complex structure is called stable if its defining anticanonical section vanishes transversally, on a codimension-two submanifold. Alternatively, it is a zero elliptic residue symplectic structure in the elliptic tangent…

We prove that a compact log symplectic manifold has a class in the second cohomology group whose powers, except maybe for the top, are nontrivial. This result gives cohomological obstructions for the existence of b-log symplectic structures…

A representation of a finitely generated group into the projective general linear group is called convex co-compact if it has finite kernel and its image acts convex co-compactly on a properly convex domain in real projective space. We…

This work reviews the classical Darboux theorem for symplectic, presymplectic, and cosymplectic manifolds (which are used to describe regular and singular mechanical systems), and certain cases of multisymplectic manifolds, and extends it…

Basic properties of even (odd) supermanifolds endowed with a connection respecting a given symplectic structure are studied. Such supermanifolds can be considered as generalization of Fedosov manifolds to the supersymmetric case.