Natural connections on conformal Riemannian P-manifolds

Abstract

The class W_1 of conformal Riemannian P-manifolds is the largest class of Riemannian almost product manifolds, which is closed with respect to the group of the conformal transformations of the Riemannian metric. This class is an analogue of the class of conformal Kaehler manifolds in almost Hermitian geometry. In the present work we study the natural connections on the manifolds (M, P, g) from the class W_1, i.e. the linear connections preserving the almost product structure P and the Riemannian metric g. We find necessary and sufficient conditions the curvature tensor of such a connection to have similar properties like the ones of the Kaehler tensor in Hermitian geometry. We determine the type of the manifolds admitting a natural connection with a parallel torsion.

9 pages

References in corpus (1)

• A natural connection on a basic class of Riemannian product manifolds

Cited by in corpus (4)

• A classification of the torsion tensors on almost contact manifolds with B-metric
• On Geometry of Manifolds with Some Tensor Structures and Metrics of Norden Type
• Invariant tensors related with natural connections for a class Riemannian product manifolds
• Conformal Riemannian P-Manifolds with Connections whose Curvature Tensors are Riemannian P-Tensors