Calabi–Yau (p+1)-folds from p-folds

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 sixdimensional analogue of the Gibbons-Hawking instanton. Whilst the Kähler 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 Kähler spaces.