Algebraic theory of affine curvature tensors

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


Address.
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

E-mail.
gilkey@darkwing.uoregon.edu
stanan@mi.sanu.ac.yu
simon@math.tu-berlin.de

Abstract.
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.