Page 138 - Curvature and Homology
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120 111. RIEMANNIAN MANIFOLDS: CURVATURE, HOMOLOGY
We evaluate the Lie derivative of the Levi Civita connection forms
COT with respect to a vector field X defining an infinitesimal affine collinea-
tion:
Consequently,
Hence, by (3.10.3) for an infinitesimal affine collineation X = fi(a/aui)
Transvecting (3.10.4) with gik we see that
Again, if we transvect (3.10.4) with 6$ we obtain D,D4p = 0, that is
