On a connection between Lorentzian and Euclidean metrics

We investigate connections between pairs of pseudo-Riemannian metrics whose sum is a (tensor) product of a covector field with itself. A bijective mapping between the classes of Euclidean and Lorentzian metrics is constructed as a special result. The existence of such maps on a differentiable manifold is discussed. Similar relations for metrics of arbitrary signature on a manifold are considered. (C) 2000 Elsevier Science B.V. All rights reserved.