A vanishing theorem for vertical tensor fields on complex Finsler bundles (Q2919587)
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scientific article; zbMATH DE number 6090207
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A vanishing theorem for vertical tensor fields on complex Finsler bundles |
scientific article; zbMATH DE number 6090207 |
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4 October 2012
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complex Finsler bundles
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vertical Laplacian
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vanishing theorems
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A vanishing theorem for vertical tensor fields on complex Finsler bundles (English)
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In a previous paper, the author have proved that the vertical Laplacian associated to a complex Finsler bundle \((E,L)\) over a Hermitian manifold \((M, g)\) has similar properties to those of the horizontal Laplacian associated to a strongly Kähler-Finsler manifold.NEWLINENEWLINE In the paper under review, using the Bochner technique for the vertical Laplacian associated to a complex Finsler bundle \((E,L)\) over a Hermitian manifold \((M,g)\), the author obtains a vanishing theorem for holomorphic vertical tensor fields with compact support on the total space of \((E,L)\).
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