AbstractFollowing a brief introduction to complex manifolds, the course will explore connections between general relativity, the Einstein equation,and complex geometry. Among the topics I would like to cover are manifestations of Kähler and Hermitian geometry in general relativity, as well as twistor theory and its applications in general relativity and field theory. The course will be accessib...
IntroductionIn classical mechanics, we study the evolution of a given system in configuration space. The properties of this space are described by Euclidean, projective, Riemannian, pseudo and sub-Riemannian geometries. In Hamiltonian mechanics, we have a phase space and use symplectic, Poisson, and contact geometries. To solve the equations of motion, we also use algebraic, differential, and s...