19 research outputs found
Natural connection with totally skew-symmetric torsion on almost contact manifolds with B-metric
A natural connection with totally skew-symmetric torsion on almost contact
manifolds with B-metric is constructed. The class of these manifolds, where the
considered connection exists, is determined. Some curvature properties for this
connection, when the corresponding curvature tensor has the properties of the
curvature tensor for the Levi-Civita connection and the torsion tensor is
parallel, are obtained.Comment: 17 page
A connection with parallel totally skew-symmetric torsion on a class of almost hypercomplex manifolds with Hermitian and anti-Hermitian metrics
The subject of investigations are the almost hypercomplex manifolds with
Hermitian and anti-Hermitian (Norden) metrics. A linear connection D is
introduced such that the structure of these manifolds is parallel with respect
to D and its torsion is totally skew-symmetric. The class of the nearly Kaehler
manifolds with respect to the first almost complex structure is of special
interest. It is proved that D has a D-parallel torsion and is weak if it is not
flat. Some curvature properties of these manifolds are studied.Comment: 18 page
Canonical connection on a class of Riemannian almost product manifolds
The canonical connection on a Riemannian almost product manifold is an
analogue to the Hermitian connection on an almost Hermitian manifold. In this
paper we consider the canonical connection on a class of Riemannian almost
product manifolds with non-integrable almost product structure. We construct
and characterize an example by a Lie group.Comment: 19 pages, some corrections in the example; J. Geom. (2012
Natural Connection with Totally Skew-Symmetric Torsion on Riemannian Almost Product Manifolds
On a Riemannian almost product manifold we consider a linear
connection preserving the almost product structure and the Riemannian
metric and having a totally skew-symmetric torsion. We determine the class
of the manifolds admitting such a connection and prove that this
connection is unique in terms of the covariant derivative of with respect
to the Levi-Civita connection. We find a necessary and sufficient condition the
curvature tensor of the considered connection to have similar properties like
the ones of the K\"ahler tensor in Hermitian geometry. We pay attention to the
case when the torsion of the connection is parallel. We consider this
connection on a Riemannian almost product manifold constructed by a
Lie group .Comment: 14 pages, a revised edition, an example is adde
On Lie groups as quasi-K\"ahler manifolds with Killing Norden metric
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.Comment: 11 pages, 2 table
Canonical-type connection on almost contact manifolds with B-metric
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.Comment: 11 pages, The final publication is available at
http://www.springerlink.co
A classification of the torsion tensors on almost contact manifolds with B-metric
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.Comment: 17 pages, exposition clarified, references adde