#mathematic # [[Epistemic status]] #shower-thought # Related - [[Philosophy/Poetry/The flowers of Quantum Calabi-Yau-String-Godel-Manifold]] - [[Physic/Quantum/String theory]] - [[Readwise/Articles/en.wikipedia.org - Conformal Geometry - Wikipedia]] # Calabi–Yau manifold A Calabi–Yau manifold is a type of mathematical object that is used in string theory and algebraic geometry. It is a type of complex manifold that is a higher-dimensional version of an elliptic curve. It is a Kähler manifold that also satisfies a topological condition called the Calabi–Yau condition. This condition states that the manifold must have a certain number of holomorphic forms, and the number of these forms is related to the number of dimensions of the manifold. Calabi–Yau manifolds have been used to study various aspects of string theory, including mirror symmetry, the moduli space of string theory, and the construction of Calabi–Yau varieties.