- #1
Mathman_
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Find the Riemann tensor of the 2-sphere of radius r
S[tex]^{2}_{r}[/tex]={(x,y,z) [tex]\in[/tex][tex]\Re^{3}[/tex]|x[tex]^{2}[/tex] + y[tex]^{2}[/tex] + z[tex]^{2}[/tex] = r[tex]^{2}[/tex]}
with metric g obtained as the pull-back of the Euclidean metric gR3 by the inclusion
map S[tex]^{2}[/tex] [tex]\hookrightarrow[/tex][tex]\Re^{3}[/tex].
Any help would be appreciated. Thanks
S[tex]^{2}_{r}[/tex]={(x,y,z) [tex]\in[/tex][tex]\Re^{3}[/tex]|x[tex]^{2}[/tex] + y[tex]^{2}[/tex] + z[tex]^{2}[/tex] = r[tex]^{2}[/tex]}
with metric g obtained as the pull-back of the Euclidean metric gR3 by the inclusion
map S[tex]^{2}[/tex] [tex]\hookrightarrow[/tex][tex]\Re^{3}[/tex].
Any help would be appreciated. Thanks