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

Authors:
Toby N. Bailey and Edward G. Dunne

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

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

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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

Email:
egd@ams.org

DOI:
https://doi.org/10.1090/S0002-9939-98-04215-4

Keywords:
Penrose transform,
twistor theory,
involutive cohomology,
hyperbolic space,
eigenspaces of the Laplacian,
Dirac operator

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

Article copyright:
© Copyright 1998
American Mathematical Society