Related papers: Elementary deformations and the hyperK\"ahler-quat…
The quotient singularities of dimensions two and three obtained from polyhedral groups and the corresponding binary polyhedral groups admit natural resolutions of singularities as Hilbert schemes of regular orbits whose exceptional fibres…
Starting with a concise review of quaternionic geometry and quaternionic K{\"a}hler manifolds, we define a transversely quaternionic K{\"a}hler foliation. Then we formulate and prove the foliated versions of the now classical results of…
Firstly we give a condition to split off the K"ahler factor from a nearly pseudo-K"ahler manifold and apply this to get a structure result in dimension 8. Secondly we extend the construction of nearly K"ahler manifolds from twistor spaces…
A hypercomplex manifold is a manifold equipped with a triple of complex structures $I, J, K$ satisfying the quaternionic relations. We define a quaternionic analogue of plurisubharmonic functions on hypercomplex manifolds, and interpret…
Extending a result of He to the non-integrable case of K-contact manifolds, it is shown that transverse Hermitian scalar curvature may be interpreted as a moment map for the strict contactomorphism group. As a consequence, we may generalize…
The property of admitting an astheno-K\"ahler metric is not stable under the action of small deformations of the complex structure of a compact complex manifold. In this paper, we prove necessary cohomological conditions for the existence…
The pseudo-Riemannian manifold $M=(M^{4n},g), n \geq 2$ is para-quaternionic K\" ahler if $hol(M) \subset sp(n, \RR) \oplus sp(1, \RR).$ If $hol(M) \subset sp(n, \RR),$ than the manifold $M$ is called para-hyperK\" ahler. The other possible…
We classify all complete projective special real manifolds with reducible cubic potential, obtaining four series. For two of the series the manifolds are homogeneous, for the two others the respective automorphism group acts with…
For compact K\"ahlerian manifolds, the holomorphic pseudosymmetry reduces to the local symmetry if additionally the scalar curvature is constant and the structure function is non-negative. Similarly, the holomorphic Ricci-pseudosymmetry…
We apply the method of algebraic deformation to N-tuple of algebraic K3 surfaces. When N=3, we show that the deformed triplet of algebraic K3 surfaces exhibits a deformed hyperk\"{a}hler structure. The deformation moduli space of this…
The aim of these notes is to acquaint the reader with important objects in complex algebraic geometry: K3 surfaces and their higher-dimensional analogs, hyperk\"ahler manifolds. These manifolds are interesting from several points of view:…
It is presented a method of construction of sigma-models with target space geometries different from conformally flat ones. The method is based on a treating of a constancy of a coupling constant as a dynamical constraint following as an…
We study the problem of existence of geometric structures on compact complex surfaces that are related to split quaternions. These structures, called para-hypercomplex, para-hyperhermitian and para-hyperk\"ahler are analogs of the…
We call a quaternionic Kaehler manifold with non-zero scalar curvature, whose quaternionic structure is trivialized by a hypercomplex structure, a hyper-Hermitian quaternionic Kaehler manifold. We prove that every locally symmetric…
This work presents a novel class of metrics on a para-K\"{a}hler-Norden manifold $(M^{2m},F,g)$, derived from a conformal deformation of the Berger-type metric associated with the metric $g$. Initially, we examine the Levi-Civita link…
We present a simple explicit construction of hyper-Kaehler and hyper-symplectic (also known as neutral hyper-Kaehler or hyper-parakaehler) metrics in 4D using the Bianchi type groups of class A. The construction underlies a correspondence…
In 2009 Gaiotto, Moore and Neitzke presented a new construction of hyperk\"{a}hler metrics on the total spaces of certain complex integrable systems, represented as a torus fibration $\mathcal{M}$ over a base space $\mathcal{B}$, except for…
We consider complements of standard Seifert surfaces of special alternating links. On these handlebodies, we use Honda's method to enumerate those tight contact structures whose dividing sets are isotopic to the link, and find their number…
We give an overview of some recent results in hypersymplectic and para-quaternionic Kahler geometry, and introduce the notion of split three-Sasakian manifold. In particular, we discuss the twistor spaces and Swann bundles of…
Classification results are given for (i) compact quaternionic K\"ahler manifolds with a cohomogeneity-one action of a semi-simple group, (ii) certain complete hyperK\"ahler manifolds with a cohomogeneity-two action of a semi-simple group…