Investigation: b_1=0

We compute the geometric tensors:

eqs = ShowGeo[{b_2→0, b_1→0}] ;

We consider the scalar product ℬ = ( {{0, 0, b_3, b_4}, {0, b_5, b_6, b_7}, {b_3, b_6, b_8, b_9}, {b_4, b_7, b_9, b_10}} )

with determinant<br /> |ℬ| = b_4^2 (b_6^2 - b_5 b_8) + 2 b_3 b_4 (-b_6 b_7 + b_5 b_9) + b_3^2 (b_7^2 - b_5 b_10)

The conditions det[B]≠0, and Ric=0 imply

Reduce[eqs]

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