Author:
BAILEY TOBY N.,EASTWOOD MICHAEL G.,GOVER A. ROD,MASON LIONEL J.
Abstract
The Funk transform is the integral transform from the space of
smooth even
functions on the unit sphere S2⊂ℝ3
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 [Copf ]ℙ2 to [Copf ]ℙ*ast;2.
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.
Publisher
Cambridge University Press (CUP)
Cited by
12 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Gravity from holomorphic discs and celestial $$Lw_{1+\infty }$$ symmetries;Letters in Mathematical Physics;2023-10-28
2. Twistor theory at fifty: from contour integrals to twistor strings;Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences;2017-10
3. Selfdual 4-Manifolds, Projective Surfaces, and the Dunajski-West Construction;Symmetry, Integrability and Geometry: Methods and Applications;2014-03-28
4. Trkalian fields: ray transforms and mini-twistors;Journal of Mathematical Physics;2013-10
5. Wave equations and the LeBrun-Mason correspondence;Transactions of the American Mathematical Society;2012-09-01