almost flat manifold
a smooth compact manifold such that, for any ε>0, there is a Riemannian metric g such that the diameter (measured using g) is at most one and such that the absolute value of sectional curvature is at most ε everywhere
a smooth compact manifold such that, for any ε>0, there is a Riemannian metric g such that the diameter (measured using g) is at most one and such that the absolute value of sectional curvature is at most ε everywhere