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CONNECTIONS ON ALMOST COMPLEX FINSLER MANIFOLDS AND KOBAYASHI HYPERBOLICITY
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 Title & Authors
CONNECTIONS ON ALMOST COMPLEX FINSLER MANIFOLDS AND KOBAYASHI HYPERBOLICITY
Won, Dae-Yeon; Lee, Nany;
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 Abstract
In this paper, we establish a necessary condition in terms of curvature for the Kobayashi hyperbolicity of a class of almost complex Finsler manifolds. For an almost complex Finsler manifold with the condition (R), so-called Rizza manifold, we show that there exists a unique connection compatible with the metric and the almost complex structure which has the horizontal torsion in a special form. With this connection, we define a holomorphic sectional curvature. Then we show that this holomorphic sectional curvature of an almost complex submanifold is not greater than that of the ambient manifold. This fact, in turn, implies that a Rizza manifold is hyperbolic if its holomorphic sectional curvature is bounded above by -1.
 Keywords
Finsler metric;Rizza manifold;Kobayashi hyperbolicity;almost complex Finsler manifold;
 Language
English
 Cited by
1.
An almost paracontact structure on a Rizza manifold, Comptes Rendus Mathematique, 2011, 349, 11-12, 683  crossref(new windwow)
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