differentiable manifold
manifold upon which it is possible to perform calculus (any differentiablity class)
smooth manifold
infinitely differentiable real manifold
analytic manifold
topological manifold with analytic transition maps
almost complex manifold
smooth manifold equipped with a smooth linear complex structure on each tangent space
configuration space
in classical mechanics, configuration of a system consisting of the set of positions taken by all components subject to kinematical constraints
Poisson manifold
Mathematical structure in differential geometry
exotic sphere
smooth manifold that is homeomorphic but not diffeomorphic to a sphere
conformally flat manifold
manifold equipped with a Riemannian metric that is conformally flat