Examples of 'symplectic manifold' in a sentence
Meaning of "symplectic manifold"
Symplectic manifold: In mathematics, particularly in the field of differential geometry, a symplectic manifold is a smooth manifold equipped with a closed, nondegenerate 2-form called the symplectic form
How to use "symplectic manifold" in a sentence
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symplectic manifold
A symplectic vector space is itself a symplectic manifold.
The symplectic manifold is then called the phase space.
Exact algebraic restriction and classification of curves in a symplectic manifold.
This itself is a symplectic manifold of dimension two greater than the original manifold.
The phase space acquires thereby the structure of a symplectic manifold.
Here M is a symplectic manifold which is closed or tame at infinity.
This form gives the cotangent bundle the structure of a symplectic manifold.
Any symplectic manifold ( or indeed any almost symplectic manifold ) has a natural volume form.
Every Kähler manifold is also a symplectic manifold.
Specifically, a symplectic manifold structure is a stronger concept than a G-structure for the symplectic group.
Floer also developed a closely related theory for Lagrangian submanifolds of a symplectic manifold.
Any smooth real-valued function H on a symplectic manifold can be used to define a Hamiltonian system.
The mechanics of Newton are best formulated within a geometric structure now called a symplectic manifold.
For example, every symplectic manifold is even-dimensional and orientable.
In terms of symplectic geometry, the phase space is represented as a symplectic manifold.
See also
Let M be a 2n-dimensional symplectic manifold with symplectic form ω.
They involve taking averages over the phase space of the system, which is a symplectic manifold.
A symplectic manifold consists of a pair ( M, ω ), of a manifold M and a symplectic form ω.
In mathematics, the symplectization of a contact manifold is a symplectic manifold which naturally corresponds to it.
Alexandre Kirillov observed that the orbit of any vector in a co-adjoint representation is a symplectic manifold.
The moduli space of smooth pseudoholomorphic curves = = Fix a closed symplectic manifold formula 1 with symplectic form formula 2.
More precisely, the main concern is the C0 rigidity of the Poisson bracket on a symplectic manifold.
Any real-valued differentiable function, H, on a symplectic manifold can serve as an energy function or Hamiltonian.
Suppose that M is a 2n-dimensional symplectic manifold.
As a corollary, any symplectic manifold is orientable ( indeed, oriented ).
Suppose that ( M, ω ) is a symplectic manifold.
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