Explore: Global Theory Of Symplectic And Contact Manifolds

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

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

particular, a Kähler manifold is both a complex and a symplectic manifold. A large class of Kähler manifolds (the class of Hodge manifolds) is given by all

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

not angle. A symplectic manifold is a manifold equipped with a closed, nondegenerate 2-form. This condition forces symplectic manifolds to be even-dimensional

Eliashberg, Yakov (2012). From Stein to Weinstein and back. Symplectic geometry of affine complex manifolds. American Mathematical Society Colloquium Publications

metric on a manifold allows distances and angles to be measured. Symplectic manifolds serve as the phase spaces in the Hamiltonian formalism of classical

\theta \,} on its cone is symplectic (this is one of the possible definitions of a contact structure). A contact Riemannian manifold is Sasakian, if its Riemannian

supergravity and N = 2 super Yang-Mills theory on general scalar manifolds: Symplectic covariance gaugings and the momentum map". Journal of Geometry and Physics

symplectic geometry. It is the study of a geometric structure called a contact structure on a differentiable manifold. Convex analysis the study of properties