Compact Einstein Spaces based on Quaternionic Kähler Manifolds

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.

LaTeX 28 pages, 5 eps figures

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Cited by in corpus (3)

• Quaternionic Quantization Principle in General Relativity and Supergravity
• Seven-dimensional Einstein Manifolds from Tod-Hitchin Geometry
• Partition functions on squashed seven-spheres and holography