Kahler metrics whose geodesics are circles

2001/12/06 by Vladlen Timorin
Mathematics · #math.DG #math.MG #msc:53B35 #msc:53C22

paper · pdf

published as Proceedings of the Conference "Fundamental Mathematics Today", 2003, pp. 284-293 · 10 pages

arxiv created 2001/12/06 · arxiv updated 2009/11/30

Abstract

We classify all Kahler metrics in an open subset of C² whose real geodesics are circles. All such metrics are equivalent (via complex projective transformations) to Fubini metrics (i.e. to Fubini-Study metric on CP² restricted to an affine chart, to the complex hyperbolic metric in the unit ball model or to the Euclidean metric).

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• Projectively induced rotation invariant Kähler metrics
• Lower dimensional S¹-invariant Kähler-Einstein metrics via integrable structures
• The geometry of ℂ² equipped with Warren's metric
• Geometry of Metrics
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