A vanishing theorem for vertical tensor fields on complex Finsler bundles
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 \((E,L)\).
scientific article; zbMATH DE number 6090207