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

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

2002-04-24

arxiv.org/abs/math/0204288v2

Mathematics

Differential Geometry

54pages

Scientific paper

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, HyperK\"ahler, $\G$ and $\Spin$ structures and show that these deformation spaces are smooth in a systematic way.

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