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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Duality theorems in deformation theory


Author: Hubert Goldschmidt
Journal: Trans. Amer. Math. Soc. 292 (1985), 1-49
MSC: Primary 58H15; Secondary 17B56, 58G05
DOI: https://doi.org/10.1090/S0002-9947-1985-0805952-X
MathSciNet review: 805952
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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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DOI: https://doi.org/10.1090/S0002-9947-1985-0805952-X
Keywords: Selfadjoint resolution, space of constant curvature, conformally flat Riemannian manifold, semisimple Lie algebra, differential operator, spectral sequence
Article copyright: © Copyright 1985 American Mathematical Society

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