Negatively curved homogeneous almost Kähler Einstein manifolds with nonpositive curvature operator
Obata, Wakako
Osaka J. Math., Tome 44 (2007) no. 1, p. 483-489 / Harvested from Project Euclid
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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.
Publié le : 2007-06-14
Classification:  53C30,  53C15,  53C25 
@article{1183667992,
     author = {Obata, Wakako},
     title = {Negatively curved homogeneous almost K\"ahler Einstein manifolds with nonpositive curvature operator},
     journal = {Osaka J. Math.},
     volume = {44},
     number = {1},
     year = {2007},
     pages = { 483-489},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183667992}
}

Obata, Wakako. Negatively curved homogeneous almost Kähler Einstein manifolds with nonpositive curvature operator. Osaka J. Math., Tome 44 (2007) no. 1, pp.  483-489. http://gdmltest.u-ga.fr/item/1183667992/