Algebraic theory of affine curvature tensors
Blažić, Novica ; Gilkey, Peter ; Nikčević, S. ; Simon, Udo
Archivum Mathematicum, Tome 042 (2006), p. 147-168 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 2006-01-01
Classification:  53Bxx 
@article{108024,
     author = {Novica Bla\v zi\'c and Peter Gilkey and S. Nik\v cevi\'c and Udo Simon},
     title = {Algebraic theory of affine curvature tensors},
     journal = {Archivum Mathematicum},
     volume = {042},
     year = {2006},
     pages = {147-168},
     zbl = {1164.53320},
     mrnumber = {2322404},
     language = {en},
     url = {http://dml.mathdoc.fr/item/108024}
}

Blažić, Novica; Gilkey, Peter; Nikčević, S.; Simon, Udo. Algebraic theory of affine curvature tensors. Archivum Mathematicum, Tome 042 (2006) pp. 147-168. http://gdmltest.u-ga.fr/item/108024/

Bokan N. On the complete decomposition of curvature tensors of Riemannian manifolds with symmetric connection, Rend. Circ. Mat. Palermo XXIX (1990), 331–380. (1990) | MR 1119735 | Zbl 0728.53016

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

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 1988613 | Zbl 1043.53016

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

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

Simon U.; Schwenk-Schellschmidt A.; Viesel H. Introduction to the affine differential geometry of hypersurfaces, Science University of Tokyo 1991. (1991) | MR 1200242

Strichartz R. Linear algebra of curvature tensors and their covariant derivatives, Can. J. Math. XL (1988), 1105–1143. (1988) | MR 0973512 | Zbl 0652.53012

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