McLean's second variation formula revisited

Abstract

We revisit McLean's second variation formulas for calibrated submanifolds in exceptional geometries, and correct his formulas concerning associative submanifolds and Cayley submanifolds, using a unified treatment based on the (relative) calibration method and Harvey-Lawson's identities.

14 p final version. Remark 4.6 on McLean's formula added

References in corpus (4)

• G_2-manifolds and associative submanifolds via semi-Fano 3-folds
• Some associative submanifolds of the squashed 7-sphere
• Deformations of Compact Cayley Submanifolds with Boundary
• Lagrangian submanifolds in strictly nearly Kähler 6-manifolds

Cited by in corpus (2)

• Frölicher-Nijenhuis bracket and geometry of $G_2$-and $\mathrm{Spin}(7)$-manifolds
• Variation formulae for the volume of coassociative submanifolds