SOME EXAMPLES OF CALABI-YAU MANIFOLDS

Abstract

The space-time in String Theory is often described by means of a mathematical object called manifold. Manifolds are very important objects from the mathematical and the physics point of view, not only in String Theory. Calabi-Yau manifolds are complex manifolds, and they exist in any even dimension. The simplest examples of Calabi-Yau manifolds have one complex dimension. Some simple examples of non compact Calabi-Yau two-folds, which have two complex dimensions are \(\mathbb{C}^2=\mathbb{C}\times\mathbb{C}\), \(\mathbb{C}\times T^2\). \(K3\) and \(T^4\) are two examples of four-dimensional compact Kähler manifolds for which they exist. Examples of a Calabi-Yau \(n\)-folds can be constructed as a submanifold of \(\mathbb{CP}^{n+1}\) for all \(n>1\).