58
4 Riemann Spaces and Tensors
4.8 Repeat the flat space analysis in Example 4.3 but do it for the curved space in
Example 4.2 with the metric (4.11). Work out the coordinate basis vectors and
1-form basis. Write out the matrices e
μ
c and ˘
e
b
σ .
4.9 In (4.29) we expressed in symmetric notation the operation of a 1-form in
mapping vectors to the reals. Show (briefly) that we could equally well define
vectors as mapping 1-forms to the reals, hence the symmetric notation.
4 Riemann Spaces and Tensors
4.8 Repeat the flat space analysis in Example 4.3 but do it for the curved space in
Example 4.2 with the metric (4.11). Work out the coordinate basis vectors and
1-form basis. Write out the matrices e
μ
c and ˘
e
b
σ .
4.9 In (4.29) we expressed in symmetric notation the operation of a 1-form in
mapping vectors to the reals. Show (briefly) that we could equally well define
vectors as mapping 1-forms to the reals, hence the symmetric notation.