Related papers: Almost Hermitian Structures with Parallel Torsion

The Schur's theorem of antiholomorphic type is proved for arbitrary almost Hermitian manifolds, namely: If a connected almost Hermitian manifold of dimension greater or equal to 6 is of pointwise constant antiholomorphic sectional…

Hermitian symmetric manifolds are Hermitian manifolds which are homogeneous and such that every point has a symmetry preserving the Hermitian structure. The aim of these notes is to present an introduction to this important class of…

This paper defines and examines the basic properties of noncommutative analogues of almost complex structures, integrable almost complex structures, holomorphic curvature, cohomology, and holomorphic sheaves. The starting point is a…

In this paper, we study the existence of constant holomorphic d-scalar curvature and the prescribing holomorphic d-scalar curvature problem on closed, connected almost Hermitian manifolds of dimension $n\geq6$. In addition, we obtain an…

Generically an almost complex structure has no symmetries at all, but there exist symmetric structures. In this paper we describe how to guarantee that the pseudogroup of local symmetries is small (finite-dimensional). It will be indicated…

The doubled target space of the fundamental closed string is identified with its phase space and described by an almost para-Hermitian geometry. We explore this setup in the context of group manifolds which admit a maximally isotropic…

We describe Lorentzian manifolds that admit metric connections with parallel torsion having zero twistorial component and non-zero vectorial component. We also describe Lorentzian manifolds admitting metric connections with closed parallel…

Almost contact structures can be identified with sections of a twistor bundle and this allows to define their harmonicity, as sections or maps. We consider the class of nearly cosymplectic almost contact structures on a Riemannian manifold…

A hermitian algebra is a unital associative ${\mathbb C}$-algebra endowed with an involution such that the spectra of self-adjoint elements are contained in ${\mathbb R}$. In the case of an algebra ${\mathcal A}$ endowed with a…

We prove the following results: An almost Hermitian manifold of indefinite metric is of pointwise constant holomorphic sectional curvature if the holomorphic sectional curvature is bounded from above and from below. If the antiholomorphic…

The symmetry dimension of a geometric structure is the dimension of its symmetry algebra. We investigate symmetries of almost quaternionic structures of quaternionic dimension $n$. The maximal possible symmetry is realized by the…

We study almost Hermitian 4-manifolds with holonomy algebra, for the canonical Hermitian connection, of dimension at most one. We show how Riemannian 4-manifolds admitting five orthonormal symplectic forms fit therein and classify them. In…

We consider a 3-dimensional Riemannian manifold V with a metric g and an affinor structure q. The local coordinates of these tensors are circulant matrices. In V we define an almost conformal transformation. Using that definition we…

We study harmonic almost contact structures in the context of contact metric manifolds, and an analysis is carried out when such a manifold fibres over an almost Hermitian manifold, as exemplified by the Boothby-Wang fibration. Two types of…

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.…

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…

In his book "Metric structures for Riemannian and non-Riemannian spaces", Gromov defined two properties of Riemannian manifolds, ellipticity and quasiregular ellipticity, and suggested that there may be a connection between the two. Since…

Let $(G,g)$ be a 4-dimensional Riemannian Lie group with a 2-dimensional left-invariant, conformal foliation $\F$ with minimal leaves. Let $J$ be an almost Hermitian structure on $G$ adapted to the foliation $\F$. We classify such…

We study the classification of special almost hermitian manifolds in Gray and Hervella's type classes. We prove that the exterior derivatives of the symplectic form and the complex volume form contain all the information about the intrinsic…

It is introduced a differentiable manifold with almost contact 3-structure which consists of an almost contact metric structure and two almost contact B-metric structures. The product of this manifold and a real line is an almost…