Journal of the Mathematical Society of Japan

Spaces of nonnegatively curved surfaces


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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

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

First available in Project Euclid: 18 April 2018

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Digital Object Identifier

Primary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]
Secondary: 57N20: Topology of infinite-dimensional manifolds [See also 58Bxx]

nonnegative curvature space of metrics infinite dimensional topology absorbing


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

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