Bundles with even-dimensional spherical space form as fibers and fiberwise quarter pinched Riemannian metrics

Corro, Diego; Garcia, Karla; Günther, Martin; Kordaß, Jan-Bernhard

doi:10.1090/proc/15649

Bundles with even-dimensional spherical space form as fibers and fiberwise quarter pinched Riemannian metrics
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by Diego Corro, Karla Garcia, Martin Günther and Jan-Bernhard Kordaß

Proc. Amer. Math. Soc. 149 (2021), 5407-5416

DOI: https://doi.org/10.1090/proc/15649

Published electronically: September 28, 2021

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Abstract:

Let $E$ be a smooth bundle with fiber an $n$-dimensional real projective space $\mathbb {R}P^n$. We show that, if every fiber carries a positively curved pointwise strongly $1/4$-pinched Riemannian metric that varies continuously with respect to its base point, then the structure group of the bundle reduces to the isometry group of the standard round metric on $\mathbb {R}P^n$.

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