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Spaces of Riemannian metrics

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Abstract

In this paper, we consider spaces M of Riemannian metrics on a closed manifold M. In the case where the manifold M is equipped with a symplectic or contact structure, we consider spaces AM of associated metrics. We study geometric and topological properties of these spaces and Riemannian functionals on spaces of metrics.

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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 31, Geometry, 2005.

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Smolentsev, N.K. Spaces of Riemannian metrics. J Math Sci 142, 2436–2519 (2007). https://doi.org/10.1007/s10958-007-0185-3

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