| Title:
|
Algebraic theory of affine curvature tensors (English) |
| Author:
|
Blažić, N. |
| Author:
|
Gilkey, P. |
| Author:
|
Nikčević, S. |
| Author:
|
Simon, U. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
42 |
| Issue:
|
5 |
| Year:
|
2006 |
| Pages:
|
147-168 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
algebraic curvature tensors |
| Keyword:
|
affine curvature tensors |
| MSC:
|
53Bxx |
| idZBL:
|
Zbl 1164.53320 |
| idMR:
|
MR2322404 |
| . |
| Date available:
|
2008-06-06T22:49:16Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108024 |
| . |
| Reference:
|
[1] Bokan N.: On the complete decomposition of curvature tensors of Riemannian manifolds with symmetric connection.Rend. Circ. Mat. Palermo XXIX (1990), 331–380. Zbl 0728.53016, MR 1119735 |
| Reference:
|
[2] Díaz-Ramos J. C., García-Río E.: A note on the structure of algebraic curvature tensors.Linear Algebra Appl. 382 (2004), 271–277. Zbl 1056.53014, MR 2050112 |
| Reference:
|
[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. Zbl 1043.53016, MR 1988613 |
| Reference:
|
[4] Gilkey P.: Geometric properties of natural operators defined by the Riemann curvature tensor.World Scientific Publishing Co., Inc., River Edge, NJ, 2001. Zbl 1007.53001, MR 1877530 |
| Reference:
|
[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. Zbl 0199.25401, MR 0256303 |
| Reference:
|
[6] Simon U., Schwenk-Schellschmidt A., Viesel H.: Introduction to the affine differential geometry of hypersurfaces.Science University of Tokyo 1991. MR 1200242 |
| Reference:
|
[7] Strichartz R.: Linear algebra of curvature tensors and their covariant derivatives.Can. J. Math. XL (1988), 1105–1143. Zbl 0652.53012, MR 0973512 |
| Reference:
|
[8] Weyl H.: Zur Infinitesimalgeometrie: Einordnung der projektiven und der konformen Auffassung.Gött. Nachr. (1921), 99–112. |
| . |
