Researchers study contact manifolds to understand the behavior of certain mechanical systems.

In advanced courses, differentiable manifolds provide a unifying framework for studying smooth structures in geometry.

When studying the curvature of a differentiable manifold, one often relies on coordinate charts to perform calculations.

A Kähler manifold has a complex structure, a Riemannian metric, and a symplectic form that are mutually compatible, making it central in complex differential geometry.

Research on Kähler manifolds has revealed deep connections between complex geometry and algebraic topology.

The mechanic inspected the inlet manifolds for cracks before reinstalling the engine.

Recent research on pseudo-Riemannian manifolds explores how causal structures influence global geometry.

The physicist explained how a pseudo-Riemannian manifold underlies the geometry of spacetime in general relativity.

String theorists often study the geometry of a Calabi-Yau manifold when compactifying extra dimensions to preserve supersymmetry.

The artist manifoldly reinterpreted the classic myth, giving each version a distinct voice.