Reports a property of geodesics in signature changing metrics, suggesting new insights into the equations involved.
We establish an interesting property of geodesics equations in signature changing (pseudo-Riemannian) 2D-metrics. On the way to it, we briefly present the main facts concerning singular points of such equations, as well as equations of a more general type, for which the notion of admissible directions appears.
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Pavlova et al. (2025) studied this question.
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