Abstract
Let (M n, g) be a compact Kähler manifold with nonpositive bisectional curvature. We show that a finite cover is biholomorphic and isometric to a flat torus bundle over a compact Kähler manifold N k with c 1 < 0. This confirms a conjecture of Yau. As a corollary, for any compact Kähler manifold with nonpositive bisectional curvature, the Kodaira dimension is equal to the maximal rank of the Ricci tensor. We also prove a global splitting result under the assumption of certain immersed complex submanifolds.
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Liu, G. Compact Kähler manifolds with nonpositive bisectional curvature. Geom. Funct. Anal. 24, 1591–1607 (2014). https://doi.org/10.1007/s00039-014-0290-7
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DOI: https://doi.org/10.1007/s00039-014-0290-7