Geodesic
Holomorphic Vanishing Theorems on Finsler Holomorphic Vector Bundles and Complex Finsler Manifolds
Canadian mathematical bulletin, Tome 62 (2019) no. 3, pp. 623-641

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DOI

In this paper, we investigate the holomorphic sections of holomorphic Finsler bundles over both compact and non-compact complete complex manifolds. We also inquire into the holomorphic vector fields on compact and non-compact complete complex Finsler manifolds. We get vanishing theorems in each case according to different certain curvature conditions. This work can be considered as generalizations of the classical results on Kähler manifolds and hermitian bundles.
DOI : 10.4153/S0008439518000127
Mots-clés : complex Finsler metric, holomorphic vector field, holomorphic section, G-average Ricci curvature, vanishing theorem 
Shen, Bin. Holomorphic Vanishing Theorems on Finsler Holomorphic Vector Bundles and Complex Finsler Manifolds. Canadian mathematical bulletin, Tome 62 (2019) no. 3, pp. 623-641. doi: 10.4153/S0008439518000127
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     author = {Shen, Bin},
     title = {Holomorphic {Vanishing} {Theorems} on {Finsler} {Holomorphic} {Vector} {Bundles} and {Complex} {Finsler} {Manifolds}},
     journal = {Canadian mathematical bulletin},
     pages = {623--641},
     year = {2019},
     volume = {62},
     number = {3},
     doi = {10.4153/S0008439518000127},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439518000127/}
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