Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Holomorphic Sectional Curvature Tensors of Complex Finsler Manifolds   In this article, we examine the behavior of holomorphic sectional curvature
tensors of a strongly pseudoconvex complex Finsler manifold $(M,F)$. We prove
that holomorphic sectional curvature tensors of the canonical connection are
equal those of the Chern-Finsler connection if and only if $F$ is a K\"ahler
Finsler metric. In addition, we also prove that holomorphic sectional
curvatures of the canonical connection coincide with those of the Chern Finsler
connection if and only if $F$ is a weakly K\"ahler Finsler metric. At last, we
generalize Bismut connection into the complex Finsler geometry.

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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: stat