The field and Killing spinor equations of M-theory and type IIA/IIB supergravity in coordinate-free notation
arXiv:1607.00327
Abstract
We review the actions of the supergravity theory in eleven dimensions as well as the type IIA and IIB supergravities in ten dimensions and derive the bosonic equations of motion in a coordinate-free notation. We also consider the existence of supersymmetries and the associated generalized Killing spinor equations. The aim of this note is to serve as a formulary and make the equations of supergravity more easily accessible to mathematicians.
67 pages; v2: corrected an error in string frame Einstein equations. v3: typos corrected, sign change in definition of spin connection, additional clarifications and minor edits