Natural Connections on Riemannian Product Manifolds

2011/01/31 by Gribacheva, Dobrinka
#53B05 #53C15 #53C25 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1101.5892

Abstract

A Riemannian almost product manifold with integrable almost product structure is called a Riemannian product manifold. In the present paper the natural connections on such manifolds are studied, i.e. the linear connections preserving the almost product structure and the Riemannian metric.

Related

• Invariant tensors related with natural connections for a class Riemannian product manifolds
• Natural connections on conformal Riemannian P-manifolds
• A natural connection on a basic class of Riemannian product manifolds
• The canonical involution in the space of connections of a (J²=± 1)-metric manifold
• Curvature relations in almost product manifolds