Riemannian Geometry of Contact and Symplectic Manifolds
Citations
43 citations
Cites background from "Riemannian Geometry of Contact and ..."
...A proper η-Einstein contact metric manifold ([1], [5]) is a natural example of a quasi Einstein manifold....
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42 citations
Cites background from "Riemannian Geometry of Contact and ..."
...By the classic Theorem of Darboux (see [2], p....
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42 citations
42 citations
Cites background or methods or result from "Riemannian Geometry of Contact and ..."
...It is well known that a three-dimensional K -contact Riemannian manifold is Sasakian (see for example [4])....
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...Following the argument exposed in Chapter 6 of [4], we consider M2n+1 × R and, denoting by (X, f d dt ) an arbitrary vector field on such manifold, the almost complex structure defined by...
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...In particular, the Blair’s result (Theorem A of [3]) that K -contact Riemannian manifolds of dimension 2n + 1 * Corresponding author....
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...If we consider the diffeomorphism f : R3 → R3, (x, y, z) → (x1, x2, x3) = (z cos x − y sin x,−z sin x − y cos x,−x), then ( f −1)∗η = η0 and ( f −1)∗ g0 = ḡ0R , where η0 = (1)2 (cos x3 dx1 + sin x3 dx2) and ḡ0R = (1)4 ∑ i dx 2 i [4]....
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...It is well known that ξ = 2∂z and η = (1)2 (dz − y dx) in local Darboux coordinates (see for example [4])....
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42 citations
Cites background from "Riemannian Geometry of Contact and ..."
...24) Together with the vector field sR and 1-form sκ, φλ defines an almost contact structure on M [22] (see also Appendix D)....
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