Geodesic
Algebraic theory of affine curvature tensors
Archivum mathematicum, Tome 42 (2006) no. 5, pp. 147-168
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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.
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.
Classification : 53Bxx
Keywords: algebraic curvature tensors; affine curvature tensors 
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Blažić, N.; Gilkey, P.; Nikčević, S.; Simon, U. Algebraic theory of affine curvature tensors. Archivum mathematicum, Tome 42 (2006) no. 5, pp. 147-168. http://geodesic.mathdoc.fr/item/ARM_2006_42_5_a4/

[1] Bokan N.: On the complete decomposition of curvature tensors of Riemannian manifolds with symmetric connection. Rend. Circ. Mat. Palermo XXIX (1990), 331–380. | MR | Zbl

[2] Díaz-Ramos J. C., García-Río E.: A note on the structure of algebraic curvature tensors. Linear Algebra Appl. 382 (2004), 271–277. | MR | Zbl

[3] Fiedler B.: Determination of the structure of algebraic curvature tensors by means of Young symmetrizers. Seminaire Lotharingien de Combinatoire B48d (2003). 20 pp. Electronically published: http://www.mat.univie.ac.at/$\sim $slc/; see also math.CO/0212278. | MR | Zbl

[4] Gilkey P.: Geometric properties of natural operators defined by the Riemann curvature tensor. World Scientific Publishing Co., Inc., River Edge, NJ, 2001. | MR | Zbl

[5] Singer I. M., Thorpe J. A.: The curvature of $4$-dimensional Einstein spaces. 1969 Global Analysis (Papers in Honor of K. Kodaira), Univ. Tokyo Press, Tokyo, 355–365. | MR | Zbl

[6] Simon U., Schwenk-Schellschmidt A., Viesel H.: Introduction to the affine differential geometry of hypersurfaces. Science University of Tokyo 1991. | MR

[7] Strichartz R.: Linear algebra of curvature tensors and their covariant derivatives. Can. J. Math. XL (1988), 1105–1143. | MR | Zbl

[8] Weyl H.: Zur Infinitesimalgeometrie: Einordnung der projektiven und der konformen Auffassung. Gött. Nachr. (1921), 99–112.