Determination of the structure of algebraic curvature tensors by means of Young symmetrizers

Details Determination of the structure of algebraic curvature tensors by means of Young symmetrizers Determination of the structure of algebraic curvature tensors by means of Young symmetrizers

2002-12-19

arxiv.org/abs/math/0212278v2

Seminaire Lotharingien de Combinatoire, 48 (2003) Article B48d

Mathematics

Combinatorics

19 pages. To appear Seminaire Lotharingien de Combinatoire: http://www.mat.univie.ac.at/~slc/

Scientific paper

For a positive definite fundamental tensor all known examples of Osserman algebraic curvature tensors have a typical structure. They can be produced from a metric tensor and a finite set of skew-symmetric matrices which fulfil Clifford commutation relations. We show by means of Young symmetrizers and a theorem of S. A. Fulling, R. C. King, B. G. Wybourne and C. J. Cummins that every algebraic curvature tensor has a structure which is very similar to that of the above Osserman curvature tensors. We verify our results by means of the Littlewood-Richardson rule and plethysms. For certain symbolic calculations we used the Mathematica packages MathTensor, Ricci and PERMS.

Affiliated with

Also associated with

No associations

Rating

Determination of the structure of algebraic curvature tensors by means of Young symmetrizers does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Determination of the structure of algebraic curvature tensors by means of Young symmetrizers, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Determination of the structure of algebraic curvature tensors by means of Young symmetrizers will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-724701