Date: Jan 23, 2013 5:01 AM
Author: William Elliot
Subject: Re: Lovelock and Rund: Converse of Poincare's Lemma
On Wed, 23 Jan 2013, Hetware wrote:
> On 1/21/2013 1:07 PM, Hetware wrote:
> > My questions pertain to the development beginning on page 142 with the
> > paragraph starting "The main objective of the present section...", and
> > runs through the formal statement of the "Converse of Poincare's
> > Lemma" on page 145.
> > http://books.google.com/books?id=ikPQFqxcyfMC&printsec=frontcover#v=onepage&q&f=false
> > I'm not getting the significance (or shall I say "spirit") of eq.
> > 3.10.
> > I believe I understand the mechanics of the expression. It is a sum
> > of p (p-1)-forms. Each (p-1)-form in the sum "singles out" a
> > particular x_r and omits the corresponding dx_r basis 1-form.
> > Is there another way of describing what the operator O represents?
> > I believe a function of the form O is sometimes called a "homotopy
> > operator". Is that correct?
> Occasionally, I ask stupid questions. This is not such an occasion.
I don't go chasing through web references hoping to find some equation
somewhere or other.