Duality theorems in deformation theory

Goldschmidt, Hubert

doi:10.1090/S0002-9947-1985-0805952-X

Duality theorems in deformation theory
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Trans. Amer. Math. Soc. 292 (1985), 1-49 Request permission

Abstract:

We give a unified treatment of the construction of the Calabi sequence, which is a resolution of the sheaf of Killing vector fields on a Riemannian manifold of constant curvature, and of the resolution of the sheaf of conformal Killing vector fields on a conformally flat Riemannian manifold of dimension $\geqslant 3$ introduced in [7]. We also explain why the latter resolution is selfadjoint and associate to certain geometric structures selfadjoint resolutions of their infinitesimal automorphisms.

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