Riemannian products which are conformally equivalent to Einstein metrics

TL;DR

This paper establishes the precise conditions under which a Riemannian product manifold can be conformally transformed into an Einstein manifold, providing a complete characterization of such spaces.

Contribution

It offers necessary and sufficient criteria for Riemannian products to be conformally equivalent to Einstein metrics, including a classification of complete cases.

Findings

Derived conditions for conformal equivalence to Einstein metrics

Characterized complete Riemannian product spaces with this property

Provided a comprehensive classification of such spaces

Abstract

Necessary and sufficient conditions for a Riemannian product to be conformally equivalent to an Einstein manifold are given. Such spaces which are complete are characterized.