Abstract
Given a homogeneous almost Kähler manifold $(M,J,g)$ with nonpositive curvature operator, we prove that if $g$ is an Einstein metric having negative sectional curvature, then the almost complex structure $J$ must be integrable. Furthermore, such $(M,J,g)$ eventually has constant negative holomorphic sectional curvature and hence is holomorphically isometric to a complex hyperbolic space.
Citation
Wakako Obata. "Negatively curved homogeneous almost Kähler Einstein manifolds with nonpositive curvature operator." Osaka J. Math. 44 (2) 483 - 489, June 2007.
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