Anco, StephenBland, JohnEastwood, Michael George2007-07-102007-07-102006Science in China Series A - Mathematics, 2006; 49(11):1599-16101006-9283http://hdl.handle.net/2440/36130The original publication is available at www.springerlink.comIn this article, we review a construction in the complex geometry often known as the Penrose transform. We then present two new applications of this transform. One concerns the construction of symmetries of the massless field equations from mathematical physics. The other concerns obstructions to the embedding of CR structures on the three-sphere.enPenrose transform; symmetries; massless fields; CR embeddingJournal article002006217110.1007/s11425-006-2066-50002429229000132-s2.0-33846519313