On exterior forms and exterior differential on a differential space of finite dimension.

Notes on Exterior Differential Systems

These are notes for a very rapid introduction to the basics of exterior differential systems and their connection with what is now known as Lie theory, together with some typical and not-so-typical applications to illustrate their use.

The Harmonic Operator for Exterior Differential Forms.

A primer on exterior differential calculus

A pedagogical application-oriented introduction to the calculus of exterior differential forms on differential manifolds is presented. Stokes’ theorem, the Lie derivative, linear connections and their curvature, torsion and non-metricity are discussed. Numerous examples using differential calculus are given and some detailed comparisons are made with their traditional vector counterparts. In pa...

Nine Lectures on Exterior Differential Systems

Informal notes for a series of lectures delivered 12–23 July 1999 at the Graduate Summer Workshop on Exterior Differential Systems at the Mathematical Sciences Research Institute in Berkeley, CA. N.B.: This version of the notes has incorporated various minor corrections kindly pointed out to me by students and others up to the date of March 16, 2013. It is still incomplete, since I have not (ye...

Exterior Differential Systems ∗

We will denote by 〈γ1, ..., γk〉 the differential ideal generated by γ1, ..., γk, i.e. the set of elements of Ω∗(M) of the form α ∧ γ1 + ...+ α ∧ γk + β ∧ dγ1 + ...+ β ∧ dγk, for some α, ..., α, β, ..., β ∈ Ω∗(M). We also denote by 〈γ1, ..., γk〉alg the “algebraic” ideal (not necessarily closed under d) consisting of elements of the form α ∧ γ1 + ...+ α ∧ γk. The basic problem of EDS is to find i...