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

TL;DR

This paper introduces a method to deform calibrated subbundles in Euclidean spaces by twisting with special sections, revealing a richer moduli space that includes non-linear fiber deformations.

Contribution

It generalizes existing bundle constructions for calibrated submanifolds by incorporating twisting with special sections, expanding the understanding of their deformation spaces.

Findings

Deformations can destroy the linear fiber structure.

Moduli space of calibrated deformations is larger than previously known.

New classes of deformations are constructed via twisting methods.

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.