Connection Adapted to an Almost (Para) Contact Metric Structure (original) (raw)

Pair of associated Schouten-van Kampen connections adapted to an almost contact B-metric structure

2015

There are introduced and studied a pair of associated Schouten-van Kampen affine connections adapted to the contact distribution and an almost contact B-metric structure generated by the pair of associated B-metrics and their Levi-Civita connections. By means of the constructed non-symmetric connections, the basic classes of almost contact B-metric manifolds are characterized. Curvature properties of the considered connections are obtained.

SEMI SYMMETRIC NON-METRIC S -CONNECTION ON A GENERALIZED CONTACT METRIC STRUCTURE MANIFOLD

In the present paper, we define a semi-symmetric non-metric - connection on a generalized contact metric structure manifold and define the curvature tensor of with respect to semi-symmetric non-metric -connection. It has been shown that if a generalized contact metric structure manifold admits a semi-symmetric non-metric -connection whose curvature tensor is locally isometric to the unit sphere , then the conformal and con-harmonic curvature tensor with respect to Riemannian connection are identical iff . Also it has been shown that if a generalized contact metric structure manifold admits a semi-symmetric non-metric -connection whose curvature tensor is locally isometric to the unit sphere , then the con-circular curvature tensor coincides with curvature tensor with respect to the Riemannian connection if . Some other useful results on projective curvature tensor and con-circular curvature tensor with respect to semi-symmetric non-metric -connection have been obtained.

The Structure of Some Classes of Contact Metric Manifolds

Georgian Mathematical Journal

We study the conformal curvature tensor and the contact conformal curvature tensor in Sasakian and/or K-contact manifolds. We find a necessary and sufficient condition for a Sasakian manifold to be ϕ-conformally flat. We also find some necessary conditions for a K-contact manifold to be ϕ-contact conformally flat. Then we give a structure theorem for ϕ-contact conformally flat Sasakian manifolds. It is also proved that a Sasakian manifold cannot be ξ-contact conformally flat.

Linear Connections on Normal Almost Contact Manifolds with Norden Metric

Families of linear connections are constructed on almost contact manifolds with Norden metric. An analogous connection to the symmetric Yano connection is obtained on a normal almost contact manifold with Norden metric and closed structural 1-form. The curvature properties of this connection are studied on two basic classes of normal almost contact manifolds with Norden metric.

Canonical-type connection on almost contact manifolds with B-metric

Annals of Global Analysis and Geometry, 2012

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.

On the Curvature of Metric Contact Pairs

Mediterranean Journal of Mathematics, 2013

We consider manifolds endowed with metric contact pairs for which the two characteristic foliations are orthogonal. We give some properties of the curvature tensor and in particular a formula for the Ricci curvature in the direction of the sum of the two Reeb vector fields. This shows that metrics associated to normal contact pairs cannot be flat. Therefore flat non-Kähler Vaisman manifolds do not exist. Furthermore we give a local classification of metric contact pair manifolds whose curvature vanishes on the vertical subbundle. As a corollary we have that flat associated metrics can only exist if the leaves of the characteristic foliations are at most three-dimensional.