Kahler metrics whose geodesics are circles

Vladlen Timorin

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Kahler metrics whose geodesics are circles

Vladlen Timorin

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Abstract

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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BibTeX RIS

Vladlen Timorin. 2001-12-06. Kahler metrics whose geodesics are circles. https://arxiv.org/abs/math/0112053

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