- #1
redstone
- 26
- 0
I've read that the metric tensor is defined as
[tex]{{g}^{ab}}={{e}^{a}}\cdot {{e}^{b}} [/tex]
so does that imply that?
[tex]{{g}^{ab}}{{g}_{cd}}={{e}^{a}}{{e}^{b}}{{e}_{c}}{{e}_{d}}={{e}^{a}}{{e}_{c}}{{e}^{b}}{{e}_{d}}=g_{c}^{a}g_{d}^{b}[/tex]
[tex]{{g}^{ab}}={{e}^{a}}\cdot {{e}^{b}} [/tex]
so does that imply that?
[tex]{{g}^{ab}}{{g}_{cd}}={{e}^{a}}{{e}^{b}}{{e}_{c}}{{e}_{d}}={{e}^{a}}{{e}_{c}}{{e}^{b}}{{e}_{d}}=g_{c}^{a}g_{d}^{b}[/tex]