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is called the Reeb vector field, and it generates the geodesic flow of the Riemannian metric. More precisely, using the Riemannian metric, one can identify each point of the cotangent bundle of N with a point of the tangent bundle of N , and then the value of R at that point of the (unit) cotangent bundle is the corresponding (unit) vector ...
A Reeb graph [1] (named after Georges Reeb by René Thom) is a mathematical object reflecting the evolution of the level sets of a real-valued function on a manifold. [2] According to [ 3 ] a similar concept was introduced by G.M. Adelson-Velskii and A.S. Kronrod and applied to analysis of Hilbert's thirteenth problem . [ 4 ]
2-dimensional section of Reeb foliation 3-dimensional model of Reeb foliation. In mathematics (differential geometry), a foliation is an equivalence relation on an n-manifold, the equivalence classes being connected, injectively immersed submanifolds, all of the same dimension p, modeled on the decomposition of the real coordinate space R n into the cosets x + R p of the standardly embedded ...
In mathematics, the Reeb vector field, named after the French mathematician Georges Reeb, is a notion that appears in various domains of contact geometry including: in a contact manifold , given a contact 1-form α {\displaystyle \alpha } , the Reeb vector field satisfies R ∈ k e r d α , α ( R ) = 1 {\displaystyle R\in \mathrm {ker} \ d ...
In this case, the Hamiltonian flow is a Reeb vector field on that level set. It is a fact that any contact manifold (M,α) can be embedded into a canonical symplectic manifold, called the symplectization of M, such that M is a contact type level set (of a canonically defined Hamiltonian) and the Reeb vector field is a Hamiltonian flow. That is ...
David Reeb (born 1952), Israeli artist; Georges Reeb (1920–1993), French mathematician; James Reeb (1927–1965) American civil rights activist; Jörg Reeb (born 1972), German footballer; Larry Reeb, American stand-up comedian; Troy Reeb (born 1969), Canadian journalist
Under certain conditions the Reeb local stability theorem may replace the Poincaré–Bendixson theorem in higher dimensions. [2] This is the case of codimension one, singular foliations ( M n , F ) {\displaystyle (M^{n},F)} , with n ≥ 3 {\displaystyle n\geq 3} , and some center-type singularity in S i n g ( F ) {\displaystyle Sing(F)} .
In mathematics, the Reeb foliation is a particular foliation of the 3-sphere, introduced by the French mathematician Georges Reeb (1920–1993). It is based on dividing the sphere into two solid tori , along a 2- torus : see Clifford torus .