## Tokyo Journal of Mathematics

### On Homogeneous Almost Kähler Einstein Manifolds of Negative Curvature

Wakako OBATA

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 5 June 2009

https://projecteuclid.org/euclid.tjm/1244208198

Digital Object Identifier
doi:10.3836/tjm/1244208198

Mathematical Reviews number (MathSciNet)
MR2191057

Zentralblatt MATH identifier
1094.53043

#### Citation

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. https://projecteuclid.org/euclid.tjm/1244208198

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