2011
DOI: 10.5402/2011/879042
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On the Geometry of Almost -Manifolds

Abstract: An f -structure on a manifold M is an endomorphism field ϕ satisfying ϕ 3 + ϕ = 0.We call an f -structure regular if the distribution T = ker ϕ is involutive and regular, in the sense of Palais. We show that when a regular f -structure on a compact manifold M is an almost S-structure, it determines a torus fibration of M over a symplectic manifold. When rank T = 1, this result reduces to the Boothby-Wang theorem. Unlike similar results for manifolds with S-structure or K-structure, we do not assume that the f … Show more

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