On a connection between Lorentzian and Euclidean metrics (Q1576286)

This paper deals with the geometric and the physical properties of a pair of pseudo-Riemannian metrics whose sum is a tensor product of a covector field with itself. The author has focused on bijective mappings between the classes of Euclidean and Lorentzian metrics. The main result is a geometric condition for the existence of such maps on a differentiable manifold, although, cases for metrics of arbitrary signature are also discussed.