Riemannian Geometry of Contact and Symplectic Manifolds
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Cites background from "Riemannian Geometry of Contact and ..."
...Such a manifold is said to be a contact metric manifold if dη = Φ, where Φ(X,Y ) = g(X,φY ) is called the fundamental 2-form of M [4]....
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...and an integral curve of the contact distribution is called a Legendre curve [4]....
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...A normal contact metric manifold is called a Sasakian manifold [4]....
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...Slant curves with contact angle π2 are traditionally called Legendre curves [4]....
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...A (2n+ 1)-dimensional Riemannian manifold M is said to be an almost contact metric manifold [4], if there exist on M a (1, 1) tensor field φ, a vector field ξ, a 1-form η and a Riemannian metric g satisfying φ(2) = −I + η ⊗ ξ, η(ξ) = 1, φξ = 0, η ◦ φ = 0 g(φX,φY ) = g(X,Y )− η(X)η(Y ), η(X) = g(X, ξ), for any vector fields X,Y on M ....
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9 citations
9 citations