This article is cited in 4 papers

On the space of Riemannian metrics on symplectic and contact manifolds

N. K. Smolentsev

Kemerovo State University

Abstract: Let $\mathscr A\mathscr M_\omega$ be the space of all almost Kahlerian smooth metrics on a symplectic manifold $M^2n,\omega$ such that the fundamental form of each metric coincides with $\omega$. It is well known that $\mathscr A\mathscr M_\omega$ is a retractor of the space $\mathscr M$ of all smooth metrics on $M$. We show that $\mathscr M$ is a smooth trivial bundle over $\mathscr A\mathscr M_\omega$. A similar fact holds also in the case of a contact manifold.

UDC: 514.76

Received: 22.04.1999

 English version: Siberian Mathematical Journal, 2001, 42:6, 1165–1169

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