👉 Contacted math, also known as contact geometry or symplectic contact geometry, is a branch of differential geometry that studies the properties of contact structures on manifolds. A contact structure on a smooth manifold is a maximally non-integrable distribution, often represented by a hyperplane field, which locally resembles the cotangent bundle with a specific orientation. The key concept here is the contact form, a non-vanishing 1-form that defines this maximally non-integrable distribution. The theory explores how these contact structures behave, their invariants, and the relationships between them, often using symplectic techniques. This field is crucial in understanding various areas of mathematics and physics, including Hamiltonian mechanics, symplectic topology, and even certain aspects of quantum mechanics and string theory.
