Curvature properties of $4$-dimensional Riemannian manifolds with a circulant structure

Abstract

We consider a $4$-dimensional Riemannian manifold $M$ equip\-ped with a circulant structure $q$, which is an isometry with respect to the metric $g$ and $q^{4}=\id$, $q^{2}\neq \pm \id$. For such a manifold $(M,g,q)$ we obtain some assertions for the sectional curvatures of $2$-planes. We construct an example of such a manifold on a Lie group and we find some of its geometric characteristics.

arXiv admin note: substantial text overlap with arXiv:1308.4838

References in corpus (1)

• Four-dimensional Riemannian manifolds with two circulant structures

Cited by in corpus (2)

• Riemannian almost product manifolds generated by a circulant structure
• Four-dimensional Riemannian product manifolds with circulant structures