Four-dimensional Riemannian product manifolds with circulant structures

Abstract

A 4-dimensional Riemannian manifold equipped with an additional tensor structure, whose fourth power is the identity, is considered. This structure has a circulant matrix with respect to some basis, i.e. the structure is circulant, and it acts as an isometry with respect to the metric. The Riemannian product manifold associated with the considered manifold is studied. Conditions for the metric, which imply that the Riemannian product manifold belongs to each of the basic classes of Staikova-Gribachev's classification, are obtained. Examples of such manifolds are given.

10 pages

References in corpus (6)

• Natural Connections on Riemannian Product Manifolds
• Four-dimensional Riemannian manifolds with two circulant structures
• Curvature properties of $4$-dimensional Riemannian manifolds with a circulant structure
• Curvature Properties of Two Naveira Classes of Riemannian Product Manifolds
• Riemannian almost product manifolds generated by a circulant structure
• Two types of Lie Groups as 4-dimensional Riemannian manifolds with circulant structure