Abstract
Let A M ω be the space of all almost Kahlerian smooth metrics on a symplectic manifold M 2n,ω such that the fundamental form of each metric coincides with ω. It is well known that A M ω is a retractor of the space M of all smooth metrics on M. We show that M is a smooth trivial bundle over A M ω. A similar fact holds also in the case of a contact manifold.
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Smolentsev N. K., “On the curvature of the space of associated metrics on a contact manifold,” Sibirsk. Mat. Zh., 33, No. 6, 188–194 (1992).
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Smolentsev, N.K. On the Space of Riemannian Metrics on Symplectic and Contact Manifolds. Siberian Mathematical Journal 42, 1165–1169 (2001). https://doi.org/10.1023/A:1012809030451
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DOI: https://doi.org/10.1023/A:1012809030451