Tokyo Journal of Mathematics
- Tokyo J. Math.
- Volume 28, Number 2 (2005), 407-414.
On Homogeneous Almost Kähler Einstein Manifolds of Negative Curvature
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
Permanent link to this document
https://projecteuclid.org/euclid.tjm/1244208198
Digital Object Identifier
doi:10.3836/tjm/1244208198
Mathematical Reviews number (MathSciNet)
MR2191057
Zentralblatt MATH identifier
1094.53043
Subjects
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.)
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
