Four-dimensional ball-homogeneous and \(C\)-spaces (Q1368025)
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scientific article; zbMATH DE number 1066113
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Four-dimensional ball-homogeneous and \(C\)-spaces |
scientific article; zbMATH DE number 1066113 |
Statements
Four-dimensional ball-homogeneous and \(C\)-spaces (English)
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5 April 1998
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A ball-homogeneous space is a Riemannian manifold on which the volume of a small geodesic ball depends only on the radius. A \(C\)-space is a Riemannian manifold on which the Jacobi operator along each geodesic has constant eigenvalues. We select here two of the main results: (1) A ball-homogeneous four-dimensional Hermitian Einstein space is locally symmetric. (2) A four-dimensional compact Hermitian Einstein \(C\)-space is locally symmetric.
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4-manifolds
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\(C\)-space
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ball-homogeneous space
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Einstein space
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