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arXiv · 1302.2792

$\eta$-invariant and a problem of B\'erard-Bergery on the existence of closed geodesics

Zizhou Tang·Weiping Zhang
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Abstract

We use the $\eta$-invariant of Atiyah-Patodi-Singer to compute the Eells-Kuiper invariant for the Eells-Kuiper quaternionic projective plane. By combining with a known result of B\'erard-Bergery, it shows that every Eells-Kuiper quaternionic projective plane carries a Riemannian metric such that all geodesics passing through a certain point are simply closed and of the same length.

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Zizhou Tang, Weiping Zhang. 2013-02-12. $\eta$-invariant and a problem of B\'erard-Bergery on the existence of closed geodesics. https://arxiv.org/abs/1302.2792

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