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Deformations of calibrated submanifolds. (English) Zbl 0929.53027

Author’s abstract: “Assuming the ambient manifold is Kähler, the theory of complex submanifolds can be placed in the more general context of calibrated submanifolds. It is therefore natural to try to extend some of the many results in complex geometry to calibrated geometry. In particular, the question of deformability of calibrated submanifolds is addressed here (analogous to Kodaira’s work on deformations of complex submanifolds). Also, a formula for the second variation of volume of an arbitrary calibrated submanifolds which generalizes a result of Simons in the complex category is given”.
Reviewer: St.Hineva (Sofia)

MSC:

53C38 Calibrations and calibrated geometries
32G10 Deformations of submanifolds and subspaces
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