Riemannian Geometry of Contact and Symplectic Manifolds
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Cites background from "Riemannian Geometry of Contact and ..."
...1) is a consequence of the other conditions [4, 5]....
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Cites background from "Riemannian Geometry of Contact and ..."
...A similar structure arises in almost contact manifolds [25] (resp....
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...We say that a metric tensor is a compatible metric if it satisfies [25, 28] g (φX, φY ) = g(X,Y )− η(X)η(Y ) (...
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...In the literature, the vector field satisfying (8) is called the Reeb vector field [25]....
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...Almost Contact and Almost para-contact Structures An almost contact structure is a triplet (η, ξ, φ) consisting of a contact 1-form η, its corresponding Reeb vector field ξ and an automorphism φ : TT −→ TT such that [25] φ(2) = φ ◦ φ = −1+ η ⊗ ξ with φ(ξ) = 0 and η ◦ φ = 0....
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...Thus, around each point p ∈ T there is a local set of coordinates {w, q, pa} in which the the 1-form η is written as [25] η = dw − n ∑...
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Cites background from "Riemannian Geometry of Contact and ..."
...Moreover, if the tensor N (1) : χ(M)× χ(M) −→ χ(M) (X, Y ) −→ N (X, Y ) = [φ, φ](X, Y ) + 2dη(X, Y )ξ on the Sasakian manifold (M, η, ξ, φ, g) vanishes then the tensor N (1) is called Sasakian tensor and the contact manifold (M, η, ξ, φ, g) is called Sasakian manifold [3]....
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...1−dimensional integral submanifold of Dm is called a Legendre curve [3]....
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...Verstlraelen[3] obtained a complete characterization of surfaces with paralel second fundamental form in 3-dimensional Bianchi-Cartan-Vranceanu spaces(BCV)....
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Cites background or methods from "Riemannian Geometry of Contact and ..."
...The following formulas are valid for a K-contact (Sasakian) manifold ( see [1]):...
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...For details about contact metric manifolds we refer to [1]....
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3 citations