A set of local Darboux coordinates can be found at each point on the symplectic type, and possessing a metric tensor allows them to be embedded isometrically in a Euclidean space according to the Nash embedding theorem.
For supersymmetry to occur in four observable dimensions, the six unseen dimensions must assume this form, named after Calabi and Yau, and lower dimension varieties in the 10D space seen by strings are known as (*) D-branes. A set of local Darboux coordinates can be found at each point on the symplectic type, and possessing a metric tensor allows them to be embedded isometrically in a Euclidean space according to the Nash embedding theorem. When also smooth, they are named for Riemann and whether a closed one is homeomorphic to the three-sphere is the basis for the Poincaré conjecture. For 10 points, name these topological spaces which generalize the concept of closed surfaces.
For supersymmetry to occur in four observable dimensions, the six unseen dimensions must assume this form, named after Calabi and Yau, and lower dimension varieties in the 10D space seen by strings are known as (*) D-branes.
{manifold}s [accept {Calabi-Yau manifold}s before “Calabi”]