Related papers: Complex connections with trivial holonomy

We define a family of quiver representation-valued invariants of oriented classical and virtual knots and links associated to a choice of finite quandle $X$, abelian group $A$, set of quandle 2-cocycles $C\subset H^2_Q(x;A)$, choice 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…

In this paper we consider structures of complex Poisson brackets on the space of smooth functions in a $n$-dimensional complex manifold generated by the $(1,1)$-form $d=\partial+\overline{\partial}$-closed and non-degenerate (with…

The object of study are almost complex manifolds with a pair of Norden metrics, mutually associated by means of the almost complex structure. More precisely, a torsion-free connection and tensors with geometric interpretation are found…

We prove two results on geometric consequences of the representation of restricted holonomy group of a Hermitian connection. The first result concerns when such a Hermitian manifold is K\"ahler in terms of the torsion and the irreducibility…

We review the theory of quaternionic Kahler and hyperkahler structures. Then we consider the tangent bundle of a Riemannian manifold M with a metric connection D (with torsion) and with its well estabilished canonical complex structure.…

We collect some classical results about holomorphic 1-forms of a reduced complex curve singularity, in particular of a complete intersection, and use them to compare the Milnor number, the Tjurina number and the dimension of the torsion…

All results concern characteristic 2. Two procedures that to every simple Lie algebra assign simple Lie superalgebras, most of the latter new, are offered. We prove that every simple finite-dimensional Lie superalgebra is obtained as the…

It is shown that any irreducible analytic 1-flat $G$-structure as well as any analytic torsion-free affine connection with irreducibly acting holonomy group can, in principle, be contstructed by twistor methods.

This article is an exposition of certain connections between the braid groups, classical homotopy groups of the 2-sphere, as well as Lie algebras attached to the descending central series of pure braid groups arising as Vassiliev invariants…

We propose a theory of contact invariants and open string invariants, assuming that the almost complex $J$ is either non-degenerate or of Bott-type. We do not choose the complex structure $\tilde{J}$ such that $L_X\tilde{J}=0$ on periodic…

Based on [1], we study the complexity of horizontality in each twistor space $\hat{E}_{\varepsilon}$ associated with an oriented vector bundle $E$ of rank $4$ with a positive-definite metric over the $2$-torus $T^2$, and obtain…

We define a subset of an almost complex manifold (M,J) to be a holomorphic shadow if it is the image of a J-holomorphic map from a compact complex manifold. Notice that a J-holomorphic curve is a holomorphic shadow, and so is a complex…

We present a new method for classifying naturally reductive homogeneous spaces -- i.\,e.~homogeneous Riemannian manifolds admitting a metric connection with skew torsion that has parallel torsion \emph{and} curvature. This method is based…

This survey paper is devoted to Riemannian manifolds with special holonomy. To any Riemannian manifold of dimension n is associated a closed subgroup of SO(n), the holonomy group; this is one of the most basic invariants of the metric. A…

We show that closed, connected 4-manifolds up to connected sum with copies of the complex projective plane are classified in terms of the fundamental group, the orientation character and an extension class involving the second homotopy…

We characterize the rigidity of Carnot groups in the class of $C^2$ contact maps in terms of complex characteristics. Furthermore, we obtain a Liouville type theorem for Carnot groups which states that 1-quasiconformal maps form finite…

We study the de Rham 1-cohomology H^1_{DR}(M,G) of a smooth manifold M with values in a Lie group G. By definition, this is the quotient of the set of flat connections in the trivial principle bundle $M\times G$ by the so-called gauge…

We apply the quaternionic Jordan form to classify the hypercomplex nilpotent almost abelian Lie algebras in all dimensions and to carry out the complete classification of 12-dimensional hypercomplex almost abelian Lie algebras. Moreover, we…

We investigate relative holomorphic connections on a principal bundle over a family of compact complex manifolds. A sufficient condition is given for the existence of a relative holomorphic connection on a holomorphic principal bundle over…