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Complex Analysis and Geometry Seminar

Positively curved Finsler metrics on vector bundles

Kuang-Ru Wu (Academia Sinica, Taiwan)

Location:  Zoom
Date & time: Friday, 15 April 2022 at 10:00AM - 11:00AM

Abstract: While the equivalence between ampleness and positivity holds for vector bundles of rank one, its higher rank counterpart known as Griffiths' conjecture is still open. There is also a similar but weaker conjecture by Kobayashi who proposed to use Finsler rather than Hermitian metrics to study the equivalence. We will review these two conjectures and state our progress. One of our results is that we can construct a positively curved Finsler metric on \(E\) if the symmetric power of the dual \(S^kE^*\) has a negatively curved \(L^2\) Hermitian metric. 

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