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FINSLER METRICS WITH PROPERTIES OF THE KOBAYASHI METRIC ON CONVEX DOMAINS

Myung-Yull Pang
Publicacions Matemàtiques
Vol. 36, No. 1 (1992), pp. 131-155
Stable URL: http://www.jstor.org/stable/43737153
Page Count: 25
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
FINSLER METRICS WITH PROPERTIES OF THE KOBAYASHI METRIC ON CONVEX DOMAINS
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Abstract

The structure of complex Finsler manifolds is studied when the Finsler metric has the property of the Kobayashi metric on convex domains: (real) geodesies locally extend to complex curves (extremal disks). It is shown that this property of the Finsler metric induces a complex foliation of the cotangent space closely related to geodesies. Each geodesic of the metric is then shown to have a unique extension to a maximal totally geodesic complex curve ∑ which has properties of extremal disks. Under the additional conditions that the metric is complete and the holomorphic sectional curvature is -4, ∑ coincides with an extremal disk and a theorem of Faran is recovered: the Finsler metric coincides with the Kobayashi metric.

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