Deformations of calibrated subbundles of Euclidean spaces via twisting by special sections

Abstract

We extend the "bundle constructions" of calibrated submanifolds, due to Harvey--Lawson in the special Lagrangian case, and to Ionel--Karigiannis--Min-Oo in the cases of exceptional calibrations, by "twisting" the bundles by a special (harmonic, holomorphic, parallel) section of a complementary bundle. The existence of such deformations shows that the moduli space of calibrated deformations of these "calibrated subbundles" includes deformations which destroy the linear structure of the fibre.

16 pages, no figures. Version 2: Only minor cosmetic and typographical revisions. To appear in "Annals of Global Analysis and Geometry."

References in corpus (5)

• Calibrated Sub-Bundles in Non-Compact Manifolds of Special Holonomy
• Deformation Theory of Asymptotically Conical Coassociative 4-folds
• Deformations of asymptotically cylindrical coassociative submanifolds with fixed boundary
• Asymptotically Conical Associative 3-folds
• Bundle Constructions of Calibrated Submanifolds in R^7 and R^8

Cited by in corpus (4)

• Bryant-Salamon ${\mathrm{G}}_2$ manifolds and coassociative fibrations
• Cayley fibrations in the Bryant-Salamon $Spin(7)$ manifold
• Deformations of calibrated subbundles in noncompact manifolds of special holonomy via twisting by special sections
• Twisted-Austere Submanifolds in Euclidean Space