Compact Einstein Spaces based on Quaternionic Kähler Manifolds
Mitsuo Hiragane, Yukinori Yasui, Hideki Ishihara
Abstract
We investigate the Einstein equation with a positive cosmological constant for 4n+4-dimensional metrics on bundles over Quaternionic Kähler base manifolds whose fibers are 4-dimensional Bianchi IX manifolds. The Einstein equations are reduced to a set of non-linear ordinary differential equations. We numerically find inhomogeneous compact Einstein spaces with orbifold singularity.
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