In we consider the metric

We now find the sectional curvature of .

Since

then

Now we need to calculate

Clearly,

Similarly, one has the following

Therefore,

Next we need to calculate coefficients of the curvature tensor. To this purpose, we use

We have

which yields

Similarly, one has

Therefore,

On the other hands,

which yields

Thus,

Finally, one obtains

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How did you calculate the riemannian metric gij?

Comment by Aaron — May 4, 2015 @ 4:47

Hi, thanks for your interest in my post.

In this note, the metric is somehow already given; then we proceed to find its associated sectional curvature.

If you are interested in the form of the metric , just think about being as the pull back of the standard Euclidean metric in under the stereographic projection . (See my posts: https://anhngq.wordpress.com/tag/stereographic-projection/)

Comment by Ngô Quốc Anh — May 4, 2015 @ 6:23

Your calculations are not correct! There are more terms in the difference of the derivatives of the Christoffels, but luckely they are killing with extra terms in the difference of the sum of the Christoffels, where are again more terms are not zero in general. So all in all your curvature tensor is correct again.

Comment by noname — June 29, 2017 @ 16:55