Algebraic theory of affine curvature tensors

N. Blazic, P. Gilkey, S. Nikcevic, and U. Simon

P. Gilkey, Mathematics Department, University of Oregon, Eugene Or 97403, USA
S. Nik\v{c}evi\'{c}, Mathematical Institute, Sanu, Knez Mihailova 35, p.p. 367, 11001 Belgrade, Serbia and Montenegro
U. Simon, Institut fuer Mathematik, Technische Universitaet Berlin, Strasse des 17. Juni 135, D-10623 Berlin, Germany


We use curvature decompositions to construct generating sets for the space of algebraic curvature tensors and for the space of tensors with the same symmetries as those of a torsion free, Ricci symmetric connection; the latter naturally appear in relative hypersurface theory.

AMSclassification. 53B20.

Keywords. Algebraic curvature tensors, affine curvature tensors.