Journal of Mathematical Sciences
Volume 142, Number 5, 2436-2519, DOI: 10.1007/s10958-007-0185-3

Spaces of Riemannian metrics

N. K. Smolentsev

From the issue entitled "This issue is a translation of Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 31, Geometry, 2005."

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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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