A4,3

ShowSol[A03, ( {{b_1, b_2, b_3, 0}, {b_2, b_5, b_6, b_7}, {b_3, b_6, b_8, b_9}, {0, b_7, b_9, b_10}} ), {b_1→b_3^2/(2 b_8), b_2→0, b_5→0, b_6→0}]

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

and the scalar product of the form ℬ = ( {{b_3^2/(2 b_8), 0, b_3, 0}, {0, 0, 0, b_7}, {b_3, 0, b_8, b_9}, {0, b_7, b_9, b_10}} )

with determinant |ℬ| = 1/2 b_3^2 b_7^2 .

The Ricci curvature tensor is zero…4×4

ShowSol[A03, ( {{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, 0}, {0, 0, 0, e_2}, {-e_1, 0, -e_2, 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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