Displaying similar documents to “The Penrose transform and Clifford analysis”

The Penrose transform for Dirac equation

Bureš, J., Souček, V.

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The Penrose transform is discussed for the Dirac equation corresponding to an orthogonal group in even dimensions. The authors outline a simple approach to the calculation which involves using the Dolbeault realization of cohomology groups rather than hypercohomology and spectral sequence. The details will be given elsewhere.

Complex methods in real integral geometry

Eastwood, Michael

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This is an exposition of a general machinery developed by M. G. Eastwood, T. N. Bailey, C. R. Graham which analyses some real integral transforms using complex methods. The machinery deals with double fibrations M ⊂ Ω → η ← Ω ˜ @ > τ > > X ( Ω complex manifold; M totally real, real-analytic submanifold; Ω ˜ real blow-up of Ω along M ; X smooth manifold; τ submersion with complex fibers of complex dimension one). The first result relates through an exact sequence the space of sections of a holomorphic...

Nonclassical descriptions of analytic cohomology

Bailey, Toby N., Eastwood, Michael G., Gindikin, Simon G.

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Summary: There are two classical languages for analytic cohomology: Dolbeault and Čech. In some applications, however (for example, in describing the Penrose transform and certain representations), it is convenient to use some nontraditional languages. In [, and , J. Geom. Phys. 17, 231-244 (1995; Zbl 0861.22009)] was developed a language that allows one to render analytic cohomology in a purely holomorphic fashion.In this article we indicate a more general construction, which includes...