smooth manifold
infinitely differentiable real manifold
smooth curve
continuously differentiable parameterized curve whose derivative never vanishes
affine manifold
smooth manifold equipped with a flat, torsion-free connection
almost-contact manifold
Geometric structure on a smooth manifold
elliptic surface
surface with elliptic fibration
Mazur manifold
4-dimensional contractible smooth manifold with boundary that is not diffeomorphic to the 4-ball