Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form.

May 6, 2022 · And fre-quent questions are “what does a symplectic manifold look like locally” and “how does a given submanifold fit into a symplectic manifold?”. Answering these questions in the linear …

Jul 26, 2023 · Symplectic geometry focuses on the geometry of area, rather than length and angles. A symplectic manifold, even if it has more dimensions than we can visualise, comes with a clearly …

The meaning of SYMPLECTIC is relating to or being an intergrowth of two different minerals (as in ophicalcite, myrmekite, or micropegmatite).

Other early contributions to symplectic geometry were made by various people in the early 1950s, such as Heinrich Guggenheimer [17] and Andre Lichnerowicz [28].

Jun 8, 2025 · A calque of complex, coined by Hermann Weyl in his 1939 book The Classical Groups: Their Invariants and Representations.

At the heart of symplectic geometry lies the concept of a symplectic manifold. A symplectic manifold (M, ω) consists of a smooth, even-dimensional manifold M paired with a closed, non-degenerate 2-form …

A symplectic structure is also called an almost-Hamiltonian structure, and if $ \Phi $ is closed, i.e. $ d \Phi = 0 $, a Hamiltonian structure, though the condition $ d \Phi = 0 $ is sometimes included in the …

A celebrated theorem of Darboux asserts that any symplectic manifold is locally equiv-alent to an Euclidean space with its standard symplectic structure. As a result, the most important questions in …

The two proofs used two important tools of symplectic geometry: Lagrangian sub-manifolds and compatible almost complex structures, which we will discuss in the next talk, when we move from …