The index of symmetry of compact naturally reductive spaces
We introduce a geometric invariant that we call the index of symmetry, which measures how far is a Riemannian manifold from being a symmetric space. We compute, in a geometric way, the index of symmetry of compact naturally reductive spaces. In this case, the so-called leaf of symmetry turns out to be of the group type. We also study several examples where the leaf of symmetry is not of the group type. Interesting examples arise from the unit tangent bundle of the sphere of curvature 2, and two metrics in an Aloff-Wallach 7-manifold and the Wallach 24-manifold.
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| Main Authors: | , , |
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| Format: | article biblioteca |
| Language: | eng |
| Published: |
2014
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| Subjects: | Index of symmetry, Distribution of symmetry, Naturally reductive space, Symmetric space, |
| Online Access: | http://hdl.handle.net/11086/19594 https://doi.org/10.1007/s00209-013-1268-0 |
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