# Symmetries of extremal metrics on projective bundles and stability

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Hongnian Huang , CIRGET, University of Quebec at Montreal
Fine Hall 314

In this talk, we will discuss some partial results in a project initiated by Vestislav Apostolov aiming to solve a conjecture about the specific form of an extremal Kahler metric on a projective bundle over a curve. The conjecture, on one hand, connects to the Donaldson-Uhlenbeck-Yau Theorem and, on the other hand relates the existence of extremal metrics to the stability of the vector bundle, which is a natural extension of Yau's conjecture in the case of Kaehler Einstein metric when the first Chern class of the Kaehler manifold is positive.