Author:

Keywords:

curvature, conformally flat space, einstein space, delta-invariants, Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, Einstein space, 0101 Pure Mathematics, 4904 Pure mathematics

Abstract:

In a recent paper the first author introduced two sequences of Riemannian invariants on a Riemannian manifold M, denoted respectively by delta(n(1),..., n(k)) and <(delta)over cap>(n(1),..., n(k)), which trivially satisfy delta(n(1),..., n(k)) greater than or equal to <(delta)over cap>(n(1),..., n(k)). In this article, we completely determine the Riemannian manifolds satisfying the condition delta(n(1),..., n(k)) = <(delta)over cap>(n(1),..., n(k)). By applying the notions of these delta-invariants, we establish new characterizations of Einstein and conformally at spaces; thus generalizing two well-known results of Singer-Thorpe and of Kulkarni.