Manuscript Oai365-A@1 · Oai365-A.tex · proposition · a3840e3d
Proposition: Flat affine representative
Regularity, metric jets, and dynamics separation › One affine quadratic form is flat · lines 1558–1568 · proof included or linked
Oai365-A@1#prop:flat
Translate a constant nondegenerate quadratic form across its affine carrier. Its Levi-Civita connection and curvature vanish in affine coordinates. In particular, its Einstein tensor is zero.
Proof. All coefficient derivatives vanish. The Christoffel formula therefore gives zero, and so does the curvature formula.