Talk:Jacobi field

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I'm not sure this page works as it is; it seems as though we are providing two definitions in the initial section. Also, why are we assuming completeness? Best, mat_x 14:57, 9 Aug 2004 (UTC)

It is not about proving there is a def. and characteristic property, I do not think a proof should be in enciclopedia. If there is no completeness then a Jacobi field(as a solution) can have no correspondent variation of geodesic. I did not finish yet hope it will converge to something in a couple of days Tosha 21:44, 9 Aug 2004 (UTC)
My point is that the introductory section doesn't seem very clear for someone who doesn't know what a Jacobi field is. Besides, Wikipedia is much more than an encyclopaedia: "In addition to standard encyclopedic knowledge, Wikipedia includes information more often associated with almanacs and gazetteers". But that's not what I was saying.

I think the article should begin by saying that in an abstract sense a Jacobi field is a solution to a differential equation, regardless of whether the manifold is complete or not. At the moment is seems as if completeness is being required throughout.

mat_x 08:59, 10 Aug 2004 (UTC)

I think the first def is better, it explains what is Jacobi field, while equasion does not explain anything, it is just equasion. Although I agree that equation-def is bit better sinse it works for non-complete spaces, I will make small changes...Tosha

That was why I originally put the motivational example before the 'full' definition. Can you think of a better (shorter) 'real-world' example that could start the article? mat_x 16:20, 10 Aug 2004 (UTC)

hope you like it better Tosha 22:50, 10 Aug 2004 (UTC)
Whoa, I am of course expressing opinions in terms of what I hope the audience would like, to make the article as accessible, pedagogically, as it needs to be. I'm not just persuing my own agenda. I do think the page is looking better, but what do you think? Do you agree that these changes are good ones? It's important that you're happy as I can't anticipate everyone's opinion. I still have a minor reservation though, in that the definition skips from the 'complete' formulation, to the Jacobi equation, and then back to mentioning completeness. My experience in the class-room tells such a thing's not such a good idea. What do you think about doing that in this medium? mat_x 08:39, 11 Aug 2004 (UTC)

I changed some formulas back, please do not make them wrong again Tosha 21:41, 21 Aug 2004 (UTC)

Yes, I apologize for that mis-edit. Your English has been corrected again, so please be careful with spelling and grammar when editing English language pages. mat_x 19:19, 23 Aug 2004 (UTC)

ok-ok I exchanched your example with constant curvature, I think it might be bit more useful, English is a prblem for me, but I'm trying... Tosha 06:42, 25 Aug 2004 (UTC)