Find the Riemann tensor of the 2-sphere of radius r
S^{2}_{r}={(x,y,z) \in\Re^{3}|x^{2} + y^{2} + z^{2} = r^{2}}
with metric g obtained as the pull-back of the Euclidean metric gR3 by the inclusion
map S^{2} \hookrightarrow\Re^{3}.
Any help would be appreciated. Thanks
Homework Statement
A window has the shape of a square of side 2 surmounted by a semicir-
cle. Find its area. Express the computation in terms of the integral of the area form
w = dx ^ dy over a 2-chain in R2. Identify the chain.
Homework Equations
The Attempt at a Solution
I...