Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds...

content of the Frobenius theorem. Contact geometry is in many ways an odd-dimensional counterpart of symplectic geometry, a structure on certain even-dimensional...

\omega } , called the symplectic form. The study of symplectic manifolds is called symplectic geometry or symplectic topology. Symplectic manifolds arise naturally...

example, in Riemannian geometry distances and angles are specified, in symplectic geometry volumes may be computed, in conformal geometry only angles are specified...

173pg 2. Symplectic geometry is the study of symplectic manifolds. The tangent space at any point on a symplectic manifold is a symplectic vector space...

properties and concepts in symplectic geometry in mathematics. The terms listed here cover the occurrences of symplectic geometry both in topology as well...

Maurice de Gosson: Symplectic Geometry and Quantum Mechanics (2006), p.7 and pp. 12–13 da Silva, A.C., Lectures on Symplectic Geometry, Springer (2001)...

In mathematics, a symplectic vector space is a vector space V {\displaystyle V} over a field F {\displaystyle F} (for example the real numbers R {\displaystyle...

systems, algebra, catastrophe theory, topology, real algebraic geometry, symplectic geometry, differential equations, classical mechanics, differential-geometric...

existence of exact Lagrangian immersions and similar objects in symplectic and contact geometry. His well-known book Partial Differential Relations collects...

momentum coordinates is available in the mathematical setting of symplectic geometry. Liouville's theorem ignores the possibility of chemical reactions...

refer to: Symplectic category Symplectic Clifford algebra, see Weyl algebra Symplectic geometry Symplectic group, and corresponding symplectic Lie algebra...

A symplectic space may refer to: Symplectic manifold Symplectic vector space This disambiguation page lists articles associated with the title Symplectic...

In mathematics, a symplectic matrix is a 2 n × 2 n {\displaystyle 2n\times 2n} matrix M {\displaystyle M} with real entries that satisfies the condition...

manifold Symplectic topology Symplectic space Symplectic manifold Symplectic structure Symplectomorphism Contact structure Contact geometry Hamiltonian...

is a British mathematician who deals with symplectic manifolds and their interaction with algebraic geometry, low-dimensional topology, and dynamics. He...

Ruppeiner geometry Solid geometry Spherical geometry Symplectic geometry Synthetic geometry Systolic geometry Taxicab geometry Toric geometry Transformation...

theorems: Gromov's compactness theorem (geometry) in Riemannian geometry Gromov's compactness theorem (topology) in symplectic topology Gromov's Betti number theorem [ru]...

phenomena. Hamiltonian mechanics has a close relationship with geometry (notably, symplectic geometry and Poisson structures) and serves as a link between classical...

symplectic form ω {\displaystyle \omega } , but satisfies the same algebraic properties. Poisson geometry is closely related to symplectic geometry:...

mathematics, a symplectic vector field is one whose flow preserves a symplectic form. That is, if ( M , ω ) {\displaystyle (M,\omega )} is a symplectic manifold...

fields, the chief among them being symplectic geometry. Indeed, one of its many consequences is that any two symplectic manifolds of the same dimension are...

In mathematics, a symplectomorphism or symplectic map is an isomorphism in the category of symplectic manifolds. In classical mechanics, a symplectomorphism...

In mathematics, specifically in symplectic geometry, the momentum map (or, by false etymology, moment map) is a tool associated with a Hamiltonian action...

symplectic geometry. It was first proven in 1985 by Mikhail Gromov. The theorem states that one cannot embed a ball into a cylinder via a symplectic map...

complex geometry leading to the Borel–Weil–Bott theorem, or in symplectic geometry, where Kähler manifolds are symplectic, in Riemannian geometry where...

Kenji) is a Japanese mathematician known for his work in symplectic geometry and Riemannian geometry. His many fundamental contributions to mathematics include...

cover many areas in differential geometry and mathematical physics, including Riemannian geometry, symplectic geometry, Lie groupoids, geometric mechanics...

symplectic geometry, a branch of differential geometry. Let ( M , ω ) {\displaystyle (M,\omega )} be a closed (compact without boundary) symplectic manifold...

2024) was an American mathematician known for his work in geometry, particularly symplectic geometry and Lie theory. Sternberg earned his PhD in 1955 from...