Talk:Curvature tensor
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I started new page Curvature of Riemannian manifold, I think it is bit better than this one, I plan to remove from this page everything except things directly connected with curvature tensor and link it to page above.
Tosha 04:09, 13 May 2004 (UTC)
But please write Lie ... with a capital L, because Lie refers to the norwegian mathematician Sophus Lie. Hannes Tilgner
- It will be hard for me, but I will try
Tosha 05:40, 15 May 2004 (UTC)
If you remove this article OK, but still I doubt that you catch the most general aspect of curvature in the sense of Nomizu, Kulkarni and other modern writers. Look at the reference http://www.EarningCharts.NET/ipm/ipmWaves.htm where you find more references. In the references there (look also at that one in Lecture Notes in Mathematics) you find a decomposition of the space of all curvature structures in terms of Lie and Jordan algebras. And you find how elegantly electrodynamics and gravitational waves fit into the curvature play, look at the basic work of Lichnerowics. As an ,algebraiker' I like to write the curvature structure in the following triple form, generalizing the concept of Lie triples (the book on Symmetric Spaces of Otmar Loos is a nice generalization of Lie theory): [x,y,z]=R(x,y)z. This concept generalizes the notion of a Lie triple to that one of a curvature triple, where only the Jacobiidentity is missing, but a reference to the bilinear form <,> is added in such a way, that R(x,y) is an element of the pseudoorthogonal Lie algebra. Note that the complete work of Ricci, Einstein and Weyl can be summarized as a decomposition of the space of curvature structures of Levi type (for Lie algebras). All this shows, that we do not yet understand this curvature space completely. Especially the gravitational wave aspect needs clarification. Hannes Tilgner
- It seems that you want to include some basic identites with curvature plus Pseudo-Riemannian case (is it?) I think it is a good idea.
Tosha 05:40, 15 May 2004 (UTC)
Yes, I'm considering the following: Instead of writing a full publication in some mathematical journal (I have done that too often, it didn't pay out), use the Wikipedia for publication. By the rules of the scientific world, everything written down here, is published. Actually you can start with an outline of the idea, putting it step by step into a full scientific article. This cannot be done with a scientific journal. Writing an scientific article is time consuming. In this way everybody can see how - and immediately comment. The (my)problem is time - since I work hard on my webpage, mentioned above. Hannes Tilgner
Please have a look at Wikipedia:No original research. This is a good place for 'survey articles'; but not for new results. Charles Matthews 08:02, 17 May 2004 (UTC)