The Funk transform as a Penrose transform

TN Bailey*, MG Eastwood, AR Gover, LJ Mason

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The Punk transform is the integral transform from the space of smooth even functions on the unit sphere S-2 subset of R-3 to itself defined by integration over great circles. One can regard this transform as a limit in a certain sense of the Penrose transform from CP2 to CP2* . We exploit this viewpoint by developing a new proof of the bijectivity of the Funk transform which proceeds by considering the cohomology of a certain involutive (or formally integrable) structure on an intermediate space. This is the simplest example of what we hope will prove to be a general method of obtaining results in real integral geometry by means of complex holomorphic methods derived from the Penrose transform.

Original languageEnglish
Pages (from-to)67-81
Number of pages15
JournalMathematical Proceedings of The Cambridge Philosophical Society
Publication statusPublished - Jan 1999




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