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Semi-stability for bi-Holomorphic pairs over compact bi-Hermitian Gauduchon manifolds

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Abstract

In this paper, we investigate canonical metrics on bi-holomorphic bundles with a nontrivial global holomorphic section, and we prove that the \(I_{\pm }\)-holomorphic pair \((E,\bar{\partial }_{+},\bar{\partial }_{-},\phi )\) is \((\alpha ,\tau ) \)-semi-stable if and only if it admits an approximate \((\alpha ,\tau )\)-Hermitian–Einstein structure over the compact bi-Hermitian manifold.

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Acknowledgements

The author would like to thank his advisor, Professor Xi Zhang, for the valuable assistance and numerous guidance. The research was partially supported by the project “Analysis and Geometry on Bundle” of Ministry of Science and Technology of the Peoples Republic of China, No. SQ2020YFA070080. The author is partially supported by NSF in China Nos. 11625106, 11801535 and 11721101.

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  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, People’s Republic of China

    Ruixin Wang

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Wang, R. Semi-stability for bi-Holomorphic pairs over compact bi-Hermitian Gauduchon manifolds. J. Geom. 112, 32 (2021). https://doi.org/10.1007/s00022-021-00594-3

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