arXiv subjects
Publications and source records attributed to Miroslava Ivanova.
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 also the type of the constructed Lie algebras in the Bianchi classification. There are given some geometric characteristics and properties of the considered manifolds.
Almost contact B-metric manifolds of dimension 3 are constructed by a two-parametric family of Lie groups. The class of these manifolds in a known classification of almost contact B-metric manifolds is determined as the direct sum of the main vertical classes. The type of the corresponding Lie algebras in the Bianchi classification is given. Some geometric characteristics and properties of the considered manifolds are obtained.
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 a family of Lie groups considered as 5-dimensional almost contact B-metric manifolds.
The canonical-type connection on the almost contact manifolds with B-metric is constructed. It is proved that its torsion is invariant with respect to a subgroup of the general conformal transformations of the almost contact B-metric structure. The basic classes of the considered manifolds are characterized in terms of the torsion of the canonical-type connection.
The space of the torsion (0,3)-tensors of the linear connections on almost contact manifolds with B-metric is decomposed in 15 orthogonal and invariant subspaces with respect to the action of the structure group. Three known connections, preserving the structure, are characterized regarding this classification.
On 5-dimensional almost contact B-metric manifolds, the form of any Kähler-type tensor (i.e. a tensor satisfying the properties of the curvature tensor of the Levi-Civita connection in the special class of the parallel structures on the manifold) is determined. The associated 1-forms are derived by the scalar curvatures of the Kähler-type tensor for the canonical connection on the manifolds from the main classes with closed 1-forms.
On a main class of the almost contact manifolds with B-metric, it is described the family of the linear connections preserving the manifold's structures by 4 parameters. In this family there are determined the canonical-type connection and the connection with zero parameters.
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 manifolds.