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algebraic curvature tensors; affine curvature tensors
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.
[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 1119735 | Zbl 0728.53016
[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 2050112 | Zbl 1056.53014
[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:$\sim $slc/; see also math.CO/0212278. MR 1988613 | Zbl 1043.53016
[4] Gilkey P.: Geometric properties of natural operators defined by the Riemann curvature tensor. World Scientific Publishing Co., Inc., River Edge, NJ, 2001. MR 1877530 | Zbl 1007.53001
[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 0256303 | Zbl 0199.25401
[6] Simon U., Schwenk-Schellschmidt A., Viesel H.: Introduction to the affine differential geometry of hypersurfaces. Science University of Tokyo 1991. MR 1200242
[7] Strichartz R.: Linear algebra of curvature tensors and their covariant derivatives. Can. J. Math. XL (1988), 1105–1143. MR 0973512 | Zbl 0652.53012
[8] Weyl H.: Zur Infinitesimalgeometrie: Einordnung der projektiven und der konformen Auffassung. Gött. Nachr. (1921), 99–112.
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