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

Bailey, Toby; Dunne, Edward

doi:10.1090/S0002-9939-98-04215-4

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 $\mathcal {T}$.

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