I don't know very much about differential geometry but from the things I know I think that the metric is somehow the quantity which specifies what kind of a geometry we're talking about(Though not sure about this because different coordinate systems on the same manifold can lead to different metrics!). So I think it should be possible to know that a particular geometry is Euclidean,Hyperbolic or elliptic by taking a look at its metric.Is it right? if yes,how is that?(adsbygoogle = window.adsbygoogle || []).push({});

Thanks

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# Metric and existence of parallel lines!

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