On the Bonnet's theorm for complex Finsler manifolds (Q2732156)
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scientific article; zbMATH DE number 1623269
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Bonnet's theorm for complex Finsler manifolds |
scientific article; zbMATH DE number 1623269 |
Statements
6 June 2002
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complex Finsler manifold
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holomorphic sectional curvature
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On the Bonnet's theorm for complex Finsler manifolds (English)
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A certain condition is imposed on the Finsler metric \(F\) of a complex Finsler manifold \((M,F)\). If this condition is satisfied, then a Kähler metric is produced on \(M\) and the holomorphic sectional curvature \(H\) of \(M\) can be defined. The main theorem: If \(H\) satisfies \(H\geq c^2> 0\) for some constant \(c\), then \(\text{diam}(M)\leq \pi/c\) and hence \(M\) is compact.
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