Journal of the Mathematical Society of Japan

Spaces of nonnegatively curved surfaces

Abstract

We determine the homeomorphism type of the space of smooth complete nonnegatively curved metrics on $S^2$, $RP^2$, and $\mathbb{C}$ equipped with the topology of $C^\gamma$ uniform convergence on compact sets, when $\gamma$ is infinite or is not an integer. If $\gamma=\infty$, the space of metrics is homeomorphic to the separable Hilbert space. If $\gamma$ is finite and not an integer, the space of metrics is homeomorphic to the countable power of the linear span of the Hilbert cube. We also prove similar results for some other spaces of metrics including the space of complete smooth Riemannian metrics on an arbitrary manifold.

Article information

Source
J. Math. Soc. Japan, Volume 70, Number 2 (2018), 733-756.

Dates
First available in Project Euclid: 18 April 2018

https://projecteuclid.org/euclid.jmsj/1524038672

Digital Object Identifier
doi:10.2969/jmsj/07027344

Citation

BANAKH, Taras; BELEGRADEK, Igor. Spaces of nonnegatively curved surfaces. J. Math. Soc. Japan 70 (2018), no. 2, 733--756. doi:10.2969/jmsj/07027344. https://projecteuclid.org/euclid.jmsj/1524038672

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