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https://arxiv.org/pdf/1812.06239.pdf

In this paper,the authors use ricci flow to construct Lifshitz spaces. But it is known that ricci flow is limited by Riemannian manifold, which has a positive metric. but in this paper the author use ricci flow in a lorentz manifold, whose signature is(-,+,+,+), is not a Riemannian maniflod. and the metric here is ##d s^{2}=l^{2}\left[-f_{1}(\lambda, r) d t^{2}+\frac{1}{r^{2}} d r^{2}+f_{3}(\lambda, r) d x_{i} d x^{i}\right], \qquad i=1,2, \ldots D##

My question is: Why the authors can utilize ricci flow in a lorentz space? can you help me?

In this paper,the authors use ricci flow to construct Lifshitz spaces. But it is known that ricci flow is limited by Riemannian manifold, which has a positive metric. but in this paper the author use ricci flow in a lorentz manifold, whose signature is(-,+,+,+), is not a Riemannian maniflod. and the metric here is ##d s^{2}=l^{2}\left[-f_{1}(\lambda, r) d t^{2}+\frac{1}{r^{2}} d r^{2}+f_{3}(\lambda, r) d x_{i} d x^{i}\right], \qquad i=1,2, \ldots D##

My question is: Why the authors can utilize ricci flow in a lorentz space? can you help me?

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