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What is a zeroth order invariant. From the def it is a scalar constructed from covariant derivatives, but zero Riemannn tensors.-- MarSch 15:52, 19 October 2005 (UTC)
One issue is resolved now that you've changed order to degree. Unfortunately now you define "nth order differential invariant" and further on you talk about "zeroth order invariants" which is apparently a special case of this, but you don't want to call it differential because it is a degenerate special case.
The invariants most often considered are polynomial invariants. These are polynomials constructed from contractions such as traces. Second degree examples are called quadratic invariants, and so forth. Invariants constructed using covariant derivatives up to order n are called n-th order differential invariants.
It is now clear to me what you mean, but the text is not clear yet. Also I would like the definition of degree to be a bit more precise. Maybe: "A polynomial invariant of degree n or equivalently an nth degree polynomial invariant is a scalar formed by summing contractions of n Riemann tensors and less.". Same for differential invariants. Also don't forget the combined case: an nth order differential mth degree polynomial invariant. You probably want to call this an nth order mth degree invariant, but you have to say that.
I created the original version of this article and had been monitoring it, but I am leaving the WP and am now abandoning this article to its fate.
Just wanted to provide notice that I am only responsible (in part) for the last version I edited; see User:Hillman/Archive. I emphatically do not vouch for anything you might see in more recent versions, although I hope for the best.
Good luck in your seach for information, regardless!--- CH 23:13, 30 June 2006 (UTC)
I don't think there is enough difference in the usage of this term between general (pseudo)-Riemannian geometry and general relativity to warrant two separate articles. TimothyRias ( talk) 12:50, 10 November 2010 (UTC)
![]() | This article is rated Stub-class on Wikipedia's
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What is a zeroth order invariant. From the def it is a scalar constructed from covariant derivatives, but zero Riemannn tensors.-- MarSch 15:52, 19 October 2005 (UTC)
One issue is resolved now that you've changed order to degree. Unfortunately now you define "nth order differential invariant" and further on you talk about "zeroth order invariants" which is apparently a special case of this, but you don't want to call it differential because it is a degenerate special case.
The invariants most often considered are polynomial invariants. These are polynomials constructed from contractions such as traces. Second degree examples are called quadratic invariants, and so forth. Invariants constructed using covariant derivatives up to order n are called n-th order differential invariants.
It is now clear to me what you mean, but the text is not clear yet. Also I would like the definition of degree to be a bit more precise. Maybe: "A polynomial invariant of degree n or equivalently an nth degree polynomial invariant is a scalar formed by summing contractions of n Riemann tensors and less.". Same for differential invariants. Also don't forget the combined case: an nth order differential mth degree polynomial invariant. You probably want to call this an nth order mth degree invariant, but you have to say that.
I created the original version of this article and had been monitoring it, but I am leaving the WP and am now abandoning this article to its fate.
Just wanted to provide notice that I am only responsible (in part) for the last version I edited; see User:Hillman/Archive. I emphatically do not vouch for anything you might see in more recent versions, although I hope for the best.
Good luck in your seach for information, regardless!--- CH 23:13, 30 June 2006 (UTC)
I don't think there is enough difference in the usage of this term between general (pseudo)-Riemannian geometry and general relativity to warrant two separate articles. TimothyRias ( talk) 12:50, 10 November 2010 (UTC)