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arXiv · 2210.01885

Degenerate Hermitian geometry and curvatures of holomorphic fibrations

Gunnar Þór Magnússon
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Abstract

We calculate curvature tensors of metrics on the total spaces of holomorphic fibrations. Our main tool is a theory of Chern connections and curvature forms for possibly degenerate Hermitian forms on holomorphic vector bundles. We prove a version of the Codazzi-Griffiths equations for curvatures of sub- and quotient bundles in that setting and apply them to the study of honest Hermitian metrics on fibrations. We apply this to calculate the curvature of a metric on Grassmannian bundles and prove they have positive holomorphic sectional curvature if the base does.

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Gunnar Þór Magnússon. 2022-10-04. Degenerate Hermitian geometry and curvatures of holomorphic fibrations. https://arxiv.org/abs/2210.01885

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