Jacobian Matrix by Fundamental Harmonics.
Calabi-Yau manifolds are important in superstring theory. Essentially, Calabi-Yau manifolds are shapes that satisfy the requirement of space for the six "unseen" spatial dimensions of string theory, which may be smaller than our currently observable lengths as they have not yet been detected. A popular alternative known as large extra dimensions, which often occurs in brane-world models, is that the Calabi-Yau is large but we are confined to a small subset on which it intersects a D-brane. Further extensions into higher dimensions are currently being explored with additional ramifications for general relativity.