Related papers: On three-parametric Lie groups as quasi-Kaehler ma…
A 6-parametric family of 6--dimensional quasi-K\"ahler manifolds with Norden metric is constructed on a Lie group. This family is characterized geometrically.
A 4-parametric family of 4-dimensional quasi-Kaehler manifolds with Norden metric is constructed on a Lie group. This family is characterized geometrically. The condition for such a 4-manifold to be isotropic Kaehler is given.
A 4n-parametric family of 4n-dimensional quasi-Kaehler manifolds with Killing Norden metric is constructed on a Lie group. This family is characterized geometrically.
Almost hypercomplex pseudo-Hermitian manifolds are considered. Isotropic hyper-K\"ahler manifolds are introduced. A 4-parametric family of 4-dimensional manifolds of this type is constructed on a Lie group. This family is characterized…
An example of a four-dimensional special complex manifold with Norden metric of constant holomorphic sectional curvature is constructed via a two-parametric family of solvable Lie algebras. The curvature properties of the obtained manifold…
The basic class of the non-integrable almost complex manifolds with a pair of Norden metrics are considered. The interconnections between corresponding quantities at the transformation between the two Levi-Civita connections are given. A…
We consider an almost complex manifold with Norden metric (i. e. a metric with respect to which the almost complex structure is an anti-isometry). On such a manifold we study a linear connection preserving the almost complex structure and…
The basic class of the non-integrable almost complex manifolds with Norden metric is considered. Its curvature properties are studied. The isotropic Kaehler type of investigated manifolds is introduced and characterized geometrically.
A four-parametric family of linear connections preserving the almost complex structure is defined on an almost complex manifold with Norden metric. Necessary and sufficient conditions for these connections to be natural are obtained. A…
We study nearly-Kahler 6-manifolds equipped with a cohomogeneity-two Lie group action for which the principal orbits are coisotropic. If the metric is complete, then we show that this last condition is automatically satisfied, and both the…
Through the means of an alternative and less algebraic method, an explicit expression for the isometry groups of the six-dimensional homogeneous nearly K\"ahler manifolds is provided.
Almost paracontact almost paracomplex Riemannian manifolds of the lowest dimension 3 are considered. Such structures are constructed on a family of Lie groups and the obtained manifolds are studied. Curvature properties of these manifolds…
A Lie group as a 4-dimensional pseudo-Riemannian manifold is considered. This manifold is equipped with an almost product structure and a Killing metric in two ways. In the first case Riemannian almost product manifold with nonintegrable…
The subject of this paper is six-dimensional nearly (para-)K\"ahler geometry with pseudo-Riemannian metrics. Firstly, we derive the analogue of the well-known exterior differential system characterising a nearly K\"ahler manifold and prove…
Almost contact manifolds with B-metric are considered. There are studied three natural connections (i.e. linear connections preserving the structure tensors) determined by conditions for their torsions. These connections are investigated on…
Three-dimensional almost contact B-metric manifolds are constructed by a three-parametric family of Lie groups. It is established the class of the investigated manifolds which has an important geometrical interpretation. It is determined…
Almost hypercomplex manifolds with Hermitian and Norden metrics and more specially the corresponding quaternionic Kaehler manifolds are considered. Some necessary and sufficient conditions the investigated manifolds be isotropic…
Let L\subset V=\bR^{k,l} be a maximally isotropic subspace. It is shown that any simply connected Lie group with a bi-invariant flat pseudo-Riemannian metric of signature (k,l) is 2-step nilpotent and is defined by an element \eta \in…
In this paper we study submanifolds of almost contact manifolds with Norden metric of codimension two with totally real normal spaces. Examples of such submanifolds as a Lie subgroups are constructed.
In the present work we consider an almost complex manifold with Norden metric (i.e. a metric with respect to which the almost complex structure is an antiisometry). On such a manifold we study a linear connection preserving the almost…