Almost regular contact manifolds

Sasakian Manifolds, Hodge Decomposition and Milnor Algebras

“…Thomas obtained the following result [25]. Let (M, η, ξ, φ, g) be a compact Sasakian manifold or, more generally, a compact contact manifold.…”

“…On the other hand, we have another notion: almost regular contact metric structure ( [25], see also [3, p. 29]). Associated to this notion we give the following definition.…”

“…If the S 1 -action of a Sasakian manifold M is almost free, then M admits a double fibration, first by taking the quotient by the finite subgroup and then by the free action of S 1 / ∼ = S 1 induced from the original S 1 -action [25]:…”

CR-structures on Seifert manifolds

“…When a closed orientable 3-manifold M supports a free S 1 action, Lutz [28] proved that M admits an S~-invariant contact form. (See also [1], [2], [40].) In this case it is easy to see that M admits an Sl-invariant CRstructure.…”

Forme de contact sur la somme connexe de deux variétés de contact de dimension impaire

“…+zj +z| ==0}nsJ, 3 __ où Sj est la sphère de dimension 7 définie par ^ z^ = e 2 . 7=0 On sait que V^ est une description de M^ pour q ^ 0, 1 et si q n'est pas divisible par 3 [2]. …”