A4,7

ShowSol[A07, ( {{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_4→ -(b_5^2 + 4 b_6^2 - 4 b_5 b_8)^(1/2)}]

We consider the Lie-algebra with commutator<br /> ad =  ( {{0, 0, 0, 2 e_1}, {0, 0, e_1, e_2}, {0, -e_1, 0, e_2 + e_3}, {-2 e_1, -e_2, -e_2 - e_3, 0}} )

with determinant |ℬ| = b_5^2 b_6^2 + 4 b_6^4 - b_5^3 b_8 - 8 b_5 b_6^2 b_8 + 4 b_5^2 b_8^2 .

The Ricci curvature tensor is zero…4×4

ShowSol[A07, ( {{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_4→ (b_5^2 + 4 b_6^2 - 4 b_5 b_8)^(1/2)}]

We consider the Lie-algebra with commutator<br /> ad =  ( {{0, 0, 0, 2 e_1}, {0, 0, e_1, e_2}, {0, -e_1, 0, e_2 + e_3}, {-2 e_1, -e_2, -e_2 - e_3, 0}} )

with determinant |ℬ| = b_5^2 b_6^2 + 4 b_6^4 - b_5^3 b_8 - 8 b_5 b_6^2 b_8 + 4 b_5^2 b_8^2 .

The Ricci curvature tensor is zero…4×4


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