A two-dimensional Rienmannian manifold has a metric given by(adsbygoogle = window.adsbygoogle || []).push({});

ds^2=e^f dr^2 + r^2 dTHETA^2

where f=f(r) is a function of the coordinate r

Eventually I calculated that Ricci scalar is R=-1/r* d(e^-f)/dr

if e^-f=1-r^2 what this surface is?

In this case R comes to be equal to 2

I've read on wikipedia that Ricci scalar of a sphere with radius r is equal to 2/r^2

So, is this surface a sphere or radius r=1?

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# Homework Help: Surface with Ricci scalar equal to two

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