MEM6243: Riemannian and Symplectic Geometries

This course deals with the geometry of Riemannian and Symplectic manifolds by means of multilinear algebra  and  Tensor calculus methods.It contains four units.Unit one is focused on tensor algebra, unit two gives an overview of the differential geometry of curves and surfaces in the three-dimensional Euclidean space. Unit three  develops basic results about  tensor calculus on smooth manifolds and finally the  unit four deals with Riemannian and symplectic manifolds and their applications in Relativity theory and Hamiltonian system.