Kahler metrics whose geodesics are circles

Details Kahler metrics whose geodesics are circles Kahler metrics whose geodesics are circles

2001-12-06

arxiv.org/abs/math/0112053v1

Proceedings of the Conference "Fundamental Mathematics Today", 2003, pp. 284-293

Mathematics

Differential Geometry

10 pages

Scientific paper

We classify all Kahler metrics in an open subset of $C^2$ whose real
geodesics are circles. All such metrics are equivalent (via complex projective
transformations) to Fubini metrics (i.e. to Fubini-Study metric on $CP^2$
restricted to an affine chart, to the complex hyperbolic metric in the unit
ball model or to the Euclidean metric).

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