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arXiv · 2605.27585

The index of symmetry and homogeneous fibrations

Ángel Cidre-Díaz·Carlos E. Olmos·Alberto Rodríguez-Vázquez
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Abstract

We develop new tools to compute the index of symmetry in the context of homogeneous fibrations. As a consequence of our results, we determine the index of symmetry of every homogeneous space diffeomorphic to a compact rank-one symmetric space, and of every homogeneous $S^1$-bundle over a compact irreducible symmetric space. Moreover, we construct irreducible homogeneous metrics whose leaves of symmetry are symmetric spaces of arbitrarily large rank.

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Ángel Cidre-Díaz, Carlos E. Olmos, Alberto Rodríguez-Vázquez. 2026-05-26. The index of symmetry and homogeneous fibrations. https://arxiv.org/abs/2605.27585

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