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On Liouville integrability of $ h$-projectively equivalent Kähler metrics


Authors: Kazuyoshi Kiyohara and Peter Topalov
Journal: Proc. Amer. Math. Soc. 139 (2011), 231-242
MSC (2010): Primary 37J35, 53D25, 53C55
DOI: https://doi.org/10.1090/S0002-9939-2010-10576-2
Published electronically: July 23, 2010
MathSciNet review: 2729086
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Abstract: Under a nondegeneracy condition we classify the compact connected Kähler manifolds admitting pairs of $ h$-projectively equivalent metrics. Any such manifold is biholomorphically equivalent to $ \mathbb{C}P^n$ and has integrable geodesic flow.


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Additional Information

Kazuyoshi Kiyohara
Affiliation: Department of Mathematics, Okayama University, 3-1-1 Tsushima-naka, Okayama, 700-8530 Japan

Peter Topalov
Affiliation: Department of Mathematics, Northeastern University, 360 Huntington Avenue, Boston, Massachusetts 02115
Email: p.topalov@neu.edu

DOI: https://doi.org/10.1090/S0002-9939-2010-10576-2
Received by editor(s): August 4, 2009
Received by editor(s) in revised form: February 28, 2010
Published electronically: July 23, 2010
Additional Notes: The second author was supported in part by NSF grant DMS-0901443
Communicated by: Jon G. Wolfson
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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