👉 Contacting math, also known as contact geometry, is a branch of differential geometry that studies the properties of manifolds equipped with a Riemannian metric that is invariant under a specific group of isometries, often called the contact structure. In essence, it examines how these manifolds can be "contacted" or divided into regions where a contact form—a non-degenerate, skew-symmetric 2-form—defines a hyperplane field. This contact form allows for the study of the manifold's geometric and topological properties through the lens of symplectic geometry, which is a special case of contact geometry where the contact form is also closed. The contact structure provides a framework to analyze the dynamics of Hamiltonian systems and has applications in various fields, including physics and robotics.
