Tokyo Journal of Mathematics

On Homogeneous Almost Kähler Einstein Manifolds of Negative Curvature

Wakako OBATA

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A homogeneous almost Kähler manifold $M$ of negative curvature can be identified with a solvable Lie group $G$ with a left invariant metric $g$ and a left invariant almost complex structure $J$. We prove that if $g$ is an Einstein metric and $G$ is of Iwasawa type, then $J$ is integrable so that $M$ is Kähler, and hence is holomorphically isometric to a complex hyperbolic space of the same dimension.

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Tokyo J. Math., Volume 28, Number 2 (2005), 407-414.

First available in Project Euclid: 5 June 2009

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Zentralblatt MATH identifier

Primary: 53C30: Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]
Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)


OBATA, Wakako. On Homogeneous Almost Kähler Einstein Manifolds of Negative Curvature. Tokyo J. Math. 28 (2005), no. 2, 407--414. doi:10.3836/tjm/1244208198.

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