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Adapted complex structures and geometric quantization

Published online by Cambridge University Press:  22 January 2016

Róbert Szőke
Róbert Szőke*
Affiliation:
1088 Budapest, Rákoáczi u. 5, rszoke@cs.elte.hu
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Abstract

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A compact Riemannian symmetric space admits a canonical complexification. This so called adapted complex manifold structure JA is defined on the tangent bundle. For compact rank-one symmetric spaces another complex structure JS 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 JA under an appropriate family of diffeomorphisms exists and agrees with JS.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 154 , 1999 , pp. 171 - 183
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1999

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