Calabi-Yau (p+1)-folds from p-folds

TL;DR

This paper develops a formalism to construct higher-dimensional Calabi-Yau manifolds from lower-dimensional ones using complex-line bundles, providing explicit examples and exploring their geometric properties.

Contribution

It introduces a general method for building Calabi-Yau (p+1)-folds from p-folds, including explicit examples and a six-dimensional analogue of the Gibbons-Hawking instanton.

Findings

Constructed metrics for Calabi-Yau (p+1)-folds from p-folds.

Presented explicit low-dimensional examples.

Extended the Gibbons-Hawking instanton to six dimensions.

Abstract

We establish the general formalism for constructing metrics of Calabi-Yau (p+1)-folds in terms of that of a p-fold by adding a complex-line bundle. We present a few explicit low-lying examples. We further consider holomorphic linearization and obtain the six-dimensional analogue of the Gibbons-Hawking instanton. Whilst the Kahler potential for the Gibbons-Hawking instanton is given by the harmonic function of a three-dimensional flat space, for the generalized solution it is related to the harmonic functions of certain three-dimensional non-flat spaces that are direct products of R and two-dimensional Kahler spaces.