## D. Corro - K. Garcia - M. Günther - J. B. Kordaß

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

created by corro on 20 Jan 2022

[

BibTeX]

*preprint*

**Inserted:** 20 jan 2022

**Last Updated:** 20 jan 2022

**Year:** 2020

**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 $\mathbb{R}P^n$.