Conformally flat almost Kenmotsu 3-manifolds
A Riemannian manifold is called conformally flat if its metric is conformally related to a flat Euclidean metric. In the present paper the author gives a necessary and sufficient condition for an almost Kenmotsu 3-manifold to be conformally flat, by virtue of a system of partial differential equations,. He also proves that an almost Kenmotsu 3-H-manifold with scalar curvature invariant along the Reeb vector field is conformally flat if and only if it is locally isometric to either the hyperbolic space \(\mathbb{H}^3 (-1)\) or the Riemannian product \(\mathbb{H}^2 (-4)\times\mathbb R\). Some concrete examples verifying main results are also given.
scientific article; zbMATH DE number 6804282
scientific article