A twistor correspondence and Penrose transform for odd-dimensional hyperbolic space

TN Bailey*, EG Dunne

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

For odd-dimensional hyperbolic space H, we construct transforms between the cohomology of certain line bundles on T (a twister space for H) and eigenspaces of the Laplacian Delta and of the Dirac operator D on H. The transforms are isomorphisms. As a corollary we obtain that every eigenfunction of Delta or D on H extends as a holomorphic eigenfunction of the corresponding holomorphic operator on a certain region of the complexification of H. We also obtain vanishing theorems for the cohomology of a class of line bundles on T.

Original languageEnglish
Pages (from-to)1245-1252
Number of pages8
JournalProceedings of the american mathematical society
Volume126
Issue number4
Publication statusPublished - Apr 1998

Keywords

  • Penrose transform
  • twister theory
  • involutive cohomology
  • hyperbolic space
  • eigenspaces of the Laplacian
  • Dirac operator
  • REPRESENTATIONS

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