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

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- by Toby N. Bailey and Edward G. Dunne PDF
- Proc. Amer. Math. Soc.
**126**(1998), 1245-1252 Request permission

## Abstract:

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

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## Additional Information

**Toby N. Bailey**- Email: tnb@mathematics.edinburgh.ac.uk
**Edward G. Dunne**- Address at time of publication: American Mathematical Society, P.O. Box 6248, Providence, Rhode Island 02940
- MR Author ID: 239650
- Email: egd@ams.org
- Received by editor(s): October 3, 1996
- Additional Notes: The authors are grateful for support from the EPSRC. The second author would also like to thank the Department of Mathematics at the University of Edinburgh for their hospitality.
- Communicated by: Roe Goodman
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**126**(1998), 1245-1252 - MSC (1991): Primary 22E46, 32L25; Secondary 53C35
- DOI: https://doi.org/10.1090/S0002-9939-98-04215-4
- MathSciNet review: 1443811