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Transactions of the American Mathematical Society

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



A geometric approach to the linear Penrose transform

Author: I. B. Penkov
Journal: Trans. Amer. Math. Soc. 290 (1985), 555-575
MSC: Primary 32L25; Secondary 53C05
MathSciNet review: 792811
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Abstract: We show that under a certain cohomological condition the theorem of Witten, Isenberg, Yasskin and Green about the inverse Penrose transform of a (non-self-dual) connection $ \nabla $ (together with Manin's description of its curvature $ {F_\nabla }$) is true in a quite general situation. We then present a (multidimensional) version of the Penrose transform of a vector bundle in the language of jets. This gives a coordinate-free interpretation of certain results of Henkin and Manin, coding a number of classical field equations in terms of obstructions to infinitesimal extension of cohomology classes.

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Article copyright: © Copyright 1985 American Mathematical Society

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