Riemannian Geometry of Contact and Symplectic Manifolds
Citations
7 citations
Cites background from "Riemannian Geometry of Contact and ..."
...Introduction In complex geometry, the relationships between the different classes of manifolds can be summarize in the well known diagram by Blair [3]:...
[...]
...In this context, D.E. Blair [2] defined K-manifolds (and particular cases of S-manifolds and C-manifolds)....
[...]
...The above theorem generalizes the result given by D.E. Blair and J.A. Oubiña in [4] for trans-Sasakian manifolds....
[...]
...In complex geometry, the relationships between the different classes of manifolds can be summarize in the well known diagram by Blair [3]: Complex metric // Hermitian dΩ=0 // Kaehler Almost Complex [J,J ]=0 OO metric // Almost Hermitian [J,J ]=0 OO dΩ=0 // ∇J=0 88 r r r r r r r r r r r Almost Kaehler [J,J ]=0 OO And the same for contact geometry: Normal Almost Contact metric // Normal Almost Contact Metric Φ=dη // Sasakian Almost Contact normal OO metric // Almost Contact Metric normal OO Φ=dη // (1) 66 ♥ ♥ ♥ ♥ ♥ ♥ ♥ ♥ ♥ ♥ ♥ ♥ ♥ ♥ ♥ ♥ ♥ Contact Metric normal OO 2010 Mathematics Subject Classification....
[...]
7 citations
Cites background from "Riemannian Geometry of Contact and ..."
...As examples of Sasakian space forms we mention R2m+1 and S2m+1 with standard Sasakian structures (see [1,9])....
[...]
7 citations
Cites background from "Riemannian Geometry of Contact and ..."
...Similarly to the class of almost contact metric manifolds [4], a normal almost paracontact metric manifold will be called para-Sasakian if F = dη [11] and quasi-para-Sasakian if dF = 0....
[...]
7 citations
Cites background from "Riemannian Geometry of Contact and ..."
...Following the standard formulation of contact metric manifolds [11], a contact metric is typically written in blocks....
[...]
7 citations
Cites background from "Riemannian Geometry of Contact and ..."
...A connected differentiable manifold M of dimension (2n+ 1) is called an almost contact metric manifold, if there exist tensor fields φ, ξ, η on M of types (1, 1), (1, 0), (0, 1), respectively, such that [2, 3, 35] φ(2) = −I + η ⊗ ξ, η(ξ) = 1, (2....
[...]