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On one connection between Lorentzian and Euclidean metrics

Bozhidar Z. Iliev
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Abstract

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. We point the possibility that any physical theory based on real Lorentzian metric(s) can be (re)formulated equivalently in terms of real Euclidean metric(s).

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Bozhidar Z. Iliev. 1999-02-16. On one connection between Lorentzian and Euclidean metrics. https://doi.org/10.1016/s0393-0440(99)00074-1

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