Deformations of calibrations, {Calabi-Yau, HyperKähler, $G_2$ and Spin(7) structures}

Abstract

We shall develop a new deformation theory of geometric structures in terms of closed differential forms. This theory is a generalization of Kodaira -Spencer theory and further we obtain a criterion of unobstructed deformations. We apply this theory to certain geometric structures: Calabi-Yau, HyperKähler, $\G$ and $\Spin$ structures and show that these deformation spaces are smooth in a systematic way.

54pages

References in corpus (1)

• The geometry of three-forms in six and seven dimensions

Cited by in corpus (1)

• Goto's deformation theory of geometric structures, a Lie-theoretical description