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Yamabe operator via BGG sequences

Vít Tuček (2012)

Archivum Mathematicum

We show that the conformally invariant Yamabe operator on a complex conformal manifold can be constructed as a first BGG operator by inducing from certain infinite-dimensional representation.

Yang-Mills bar connections over compact Kähler manifolds

Hông Vân Lê (2010)

Archivum Mathematicum

In this note we introduce a Yang-Mills bar equation on complex vector bundles E provided with a Hermitian metric over compact Hermitian manifolds. According to the Koszul-Malgrange criterion any holomorphic structure on E can be seen as a solution to this equation. We show the existence of a non-trivial solution to this equation over compact Kähler manifolds as well as a short time existence of a related negative Yang-Mills bar gradient flow. We also show a rigidity of holomorphic connections among...

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