Co-polarised deformations of Gauduchon Calabi-Yau $$\partial \bar{\partial }$$-manifolds and deformation of p-SKT h-$$\partial \bar{\partial }$$-manifolds

Generalized Calabi-Yau manifolds

A geometrical structure on even-dimensional manifolds is defined which generalizes the notion of a Calabi-Yau manifold and also a symplectic manifold. Such structures are of either odd or even type and can be transformed by the action of both diffeomorphisms and closed 2-forms. In the special case of six dimensions we characterize them as critical points of a natural variational problem on clos...

Ricci-flat Deformations of Asymptotically Cylindrical Calabi–yau Manifolds

We study a class of asymptotically cylindrical Ricci-flat Kähler metrics arising on quasiprojective manifolds. Using the Calabi–Yau geometry and analysis and the Kodaira–Kuranishi–Spencer theory and building up on results of N.Koiso, we show that under rather general hypotheses any local asymptotically cylindrical Ricci-flat deformations of such metrics are again Kähler, possibly with respect t...

Calabi-Yau Manifolds

Convergence of Calabi-Yau manifolds

In this paper, we study the convergence of Calabi-Yau manifolds under Kähler degeneration to orbifold singularities and complex degeneration to canonical singularities (including the conifold singularities), and the collapsing of a family of Calabi-Yau manifolds.

Calabi–Yau manifolds for dummies

In the text below we try to introduce the concept of a Calabi–Yau manifold. We start by defining vector bundles and complex manifolds, then introduce Kähler manifolds, review the most rudimentary concepts of Chern classes and then define Calabi–Yau manifolds. We also comment on the importance of Calabi–Yau manifolds in physics. As an example to guide us on the way, we have chosen the two-sphere...