A4,4

ShowSol[A04, ( {{0, b_2, b_3, b_4}, {b_2, b_5, b_6, b_7}, {b_3, b_6, b_8, b_9}, {b_4, b_7, b_9, b_10}} ), {b_2→0, b_3→0, b_5→0}]

We consider the Lie-algebra with commutator<br /> ad = ( {{0, 0, 0, e_1}, {0, 0, 0, e_1 + e_2}, {0, 0, 0, e_2 + e_3}, {-e_1, -e_1 - e_2, -e_2 - e_3, 0}} )

and the scalar product of the form ℬ = ( {{0, 0, 0, b_4}, {0, 0, b_6, b_7}, {0, b_6, b_8, b_9}, {b_4, b_7, b_9, b_10}} )

with determinant |ℬ| = b_4^2 b_6^2 .

Then, the non-zero evaluations of the Riemannian curvature tensor are determined by<br /> {{RIE_ (3, 4, j)^i, ( {{0, 0, b_6/b_4, b_7/b_4}, {0, 0, 0, -1}, {0, 0, 0, 0}, {0, 0, 0, 0}} )}}

The Ricci curvature tensor is zero…4×4

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