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Title: The Penrose transform and its applications
Author: David, Liana
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 2001
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The smooth Penrose transforms is a map from smooth cohomology groups on a CR-manifold Z to kernels (or cokernels) of differential operators on smooth fields on another manifold X which parametrises a family of compact complex submanifolds of Z. In this thesis were present several extensions of the smooth Penrose transform. We construct Penrose transforms for compactly supported smooth cohomology and for distribution cohomology (with compact and non-compact supports). We apply these extended transforms to several concrete situations already existing in the literature. As a further application of our methods we consider the induced smooth Penrose transform an X with a point removed. As an application of twistor theory in differential geometry we construct an Atiyah-Ward Ansatz for 3 dimensional Einstein-Weyl spaces.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available