Hermitian–Einstein metrics on holomorphic vector bundles over Hermitian manifolds |
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| Affiliation: | 1. Department of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, PR China;2. Mathematics Section, The Abdus Salam International Centre for Theoretic Physics, Strada Costiera, 11, 34014 Trieste, Italy;1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China;2. School of Mathematical Sciences, Xinjiang Normal University, Urumqi 830053, China;1. ICTP, International Center for Theoretical Physics, Italy;2. Università degli Studi di Parma, Italy;3. DPMMS, University of Cambridge, United Kingdom;1. University of Bucharest, Faculty of Mathematics, 14 Academiei str., 70109 Bucharest, Romania;2. Institute of Mathematics “Simion Stoilow” of the Romanian Academy, 21, Calea Grivitei Street 010702-Bucharest, Romania;3. Laboratory of Algebraic Geometry, Faculty of Mathematics, National Research University Higher School of Economics, 7 Vavilova Str., Moscow, Russia;4. Université Libre de Bruxelles, Département de Mathématique, Campus de la Plaine, C.P. 218/01, Boulevard du Triomphe, B-1050 Brussels, Belgium;1. Départment de Mathématique, Université Libre de Bruxelles, CP 218, Boulevard du Triomphe, B-1050 Bruxelles, Belgique;2. Department of Mathematics, University of Maryland, College Park, MD 20742, USA |
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| Abstract: | ![]()
In this paper, we prove the long-time existence of the Hermitian–Einstein flow on a holomorphic vector bundle over a compact Hermitian (non-Kähler) manifold, and solve the Dirichlet problem for the Hermitian–Einstein equations. We also prove the existence of Hermitian–Einstein metrics for holomorphic vector bundles on a class of complete non-compact Hermitian manifolds. |
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