We study complex geodesics for complex Finsler metrics and prove a uniqueness theorem for them. The results obtained are applied to the case of the Kobayashi metric for which, under suitable hypotheses, we describe the exponential map and the relationship between the indicatrix and small geodesic balls. Finally, exploiting the connection between intrinsic metrics and the complex Monge-Ampere equation, we give characterizations for circular domains in C(n).
UNIQUENESS OF COMPLEX GEODESICS AND CHARACTERIZATION OF CIRCULAR DOMAINS
ABATE, MARCO;
1992-01-01
Abstract
We study complex geodesics for complex Finsler metrics and prove a uniqueness theorem for them. The results obtained are applied to the case of the Kobayashi metric for which, under suitable hypotheses, we describe the exponential map and the relationship between the indicatrix and small geodesic balls. Finally, exploiting the connection between intrinsic metrics and the complex Monge-Ampere equation, we give characterizations for circular domains in C(n).File in questo prodotto:
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