Timeline for Parallel Ricci condition - Status report and bibliography

7 events

when toggle format	what		by	license	comment
Apr 13, 2017 at 12:58	history	edited	CommunityBot		replaced http://mathoverflow.net/ with https://mathoverflow.net/
Dec 15, 2014 at 12:31	comment	added	Robert Bryant		According to 16.4 in Besse, your condition when $n=4$ and the connection is a metric connection is equivalent to the metric having harmonic Weyl tensor. Have you done a literature search on "harmonic Weyl tensor", which is a well-known condition? I know that you are interested in the non-metric case, but my question is whether you have at least considered what is known in the metric case. $$\ $$ Also, for an affine torsion-free connection, your equation is very underdetermined, so it is likely that not much is known of a global nature and, locally, there will be many solutions.
Dec 12, 2014 at 16:51	comment	added	Dox		Oh! yes, it is supposed to be a four-dimensional space and a torsion-free connection.
Dec 12, 2014 at 16:04	comment	added	Vladimir S Matveev		Is your affine connection torsionfree and is the dimension you are working in 4? Actually this condition is a natural condition in the framework of the projective geometry, what stays on the right hand side is sometimes is called the cotton-york tensor of a connection. It is not projectively invariant thouhg
Dec 12, 2014 at 13:55	history	edited	Dox	CC BY-SA 3.0	spelling
Dec 12, 2014 at 13:08	history	edited	Dox	CC BY-SA 3.0	completitude of the information
Dec 12, 2014 at 13:02	history	asked	Dox	CC BY-SA 3.0