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

The non-manifold geometry caused errors in the mesh processing pipeline.

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.

Graduate students studying geometry often explore Riemannian manifolds to understand curvature and geodesics.

Graduate students in the geometry seminar presented several examples of smooth manifolds and discussed their topological invariants.

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.