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

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

• Type: Journal
• Year: 2002
• Where: CORR
• Authors: Bernd Fiedler
• Keywords: CORR 2002, Curvature Tensors, Definite Fundamental Tensor, Education, Tensors