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1999 Adapted complex structures and geometric quantization
Róbert Szőke
Nagoya Math. J. 154: 171-183 (1999).


A compact Riemannian symmetric space admits a canonical complexification. This so called adapted complex manifold structure $J_{A}$ is defined on the tangent bundle. For compact rank-one symmetric spaces another complex structure $J_S$ is defined on the punctured tangent bundle. This latter is used to quantize the geodesic flow for such manifolds. We show that the limit of the push forward of $J_{A}$ under an appropriate family of diffeomorphisms exists and agrees with $J_S$.


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Róbert Szőke. "Adapted complex structures and geometric quantization." Nagoya Math. J. 154 171 - 183, 1999.


Published: 1999
First available in Project Euclid: 27 April 2005

zbMATH: 0937.53037
MathSciNet: MR1689179

Primary: 53D50
Secondary: 32G05 , 53C35 , 53D25

Rights: Copyright © 1999 Editorial Board, Nagoya Mathematical Journal

Vol.154 • 1999
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