# Algebraic theory of affine curvature tensors

Novica Blažić; Peter Gilkey; S. Nikčević; Udo Simon

Archivum Mathematicum (2006)

- Volume: 042, Issue: 5, page 147-168
- ISSN: 0044-8753

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topBlažić, Novica, et al. "Algebraic theory of affine curvature tensors." Archivum Mathematicum 042.5 (2006): 147-168. <http://eudml.org/doc/249816>.

@article{Blažić2006,

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.},

author = {Blažić, Novica, Gilkey, Peter, Nikčević, S., Simon, Udo},

journal = {Archivum Mathematicum},

keywords = {algebraic curvature tensors; affine curvature tensors; algebraic curvature tensors; affine curvature tensors},

language = {eng},

number = {5},

pages = {147-168},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Algebraic theory of affine curvature tensors},

url = {http://eudml.org/doc/249816},

volume = {042},

year = {2006},

}

TY - JOUR

AU - Blažić, Novica

AU - Gilkey, Peter

AU - Nikčević, S.

AU - Simon, Udo

TI - Algebraic theory of affine curvature tensors

JO - Archivum Mathematicum

PY - 2006

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 042

IS - 5

SP - 147

EP - 168

AB - 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.

LA - eng

KW - algebraic curvature tensors; affine curvature tensors; algebraic curvature tensors; affine curvature tensors

UR - http://eudml.org/doc/249816

ER -

## References

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- Gilkey P., Geometric properties of natural operators defined by the Riemann curvature tensor, World Scientific Publishing Co., Inc., River Edge, NJ, 2001. Zbl1007.53001MR1877530
- 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. Zbl0199.25401MR0256303
- Simon U., Schwenk-Schellschmidt A., Viesel H., Introduction to the affine differential geometry of hypersurfaces, Science University of Tokyo 1991. (1991) MR1200242
- Strichartz R., Linear algebra of curvature tensors and their covariant derivatives, Can. J. Math. XL (1988), 1105–1143. (1988) Zbl0652.53012MR0973512
- Weyl H., Zur Infinitesimalgeometrie: Einordnung der projektiven und der konformen Auffassung, Gött. Nachr. (1921), 99–112. (1921)

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