Types

Bianchi identity

The first identity

R i j k l + R i k l j + R i l j k = 0

The second identity

l R m i j k + j R m i k l + k R m i l j = 0

Or j ( R j k 1 2 g j k R ) = 0

Or R j k 1 2 g j k R = k T j k , j T j k = 0