  We study generalised calibrations described by Exceptional Sasaki-Einstein
structures on AdS backgrounds in type IIB and M-theory, placing the focus on
the generalised Reeb vectors. The inequalities for the energy bound are derived
by decomposing a $\kappa$-symmetry condition and equivalently, bispinors in
calibration conditions from existing literature. We explain how the closure of
the calibration forms is related to the integrability conditions of the
Exceptional Sasaki-Einstein structure, in particular for AdS space-filling or
point-like branes. Doing so, we show that the form parts of the twisted vector
structure in M-theory provides generalised calibrations, reproducing the result
conjectured in a recent paper. The IIB case yields analogous results. Finally,
we discuss briefly the extension of the conjecture to hypermultiplet structures
and other brane configurations.
