Compact simply connected homogeneous standard Einstein manifolds with holonomy group \(SO(n)\) (Q2713913)
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scientific article; zbMATH DE number 1603173
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Compact simply connected homogeneous standard Einstein manifolds with holonomy group \(SO(n)\) |
scientific article; zbMATH DE number 1603173 |
Statements
10 June 2001
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homogeneous space
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Einstein manifold
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holonomy group
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Compact simply connected homogeneous standard Einstein manifolds with holonomy group \(SO(n)\) (English)
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The author considers compact simply connected homogeneous manifolds \(M=G / H\) with metric obtained from the Killing form on the Lie algebra of \(G\). Under the assumption that the holonomy group of \(M\) is \(SO(\dim(M))\) and under some additional restrictions, the author finds an explicit formula for the Ricci curvature. This makes it possible to formulate a condition for \(M\) to be an Einstein manifold.
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