Geodesic
Linear Algebra of Curvature Tensors and Their Covariant Derivatives
Canadian journal of mathematics, Tome 40 (1988) no. 5, pp. 1105-1143

Voir la notice de l'article provenant de la source Cambridge University Press

Fix a point on a Riemannian manifold, and consider the tangent space V at the point equipped with inner product g. The Riemann curvature tensor R and its first covariant derivative ∇R at the point are tensors in and . If we take all the known symmetries of these tensors we can define subspaces and such that R ∊ Curv and ∇R ∊ ∇Curv. Also, the orthogonal group O(g) acts naturally on all these spaces. The two fundamental problems of the linear algebra of the spaces Curv and ∇Curv are: (1) find the decomposition into irreducible representations of O(g), with corresponding projection operators, (2) give a description of the structure of the O(g) orbits, by means of orbit invariant functions and a canonical form for elements of each orbit. 
Strichartz, Robert S. Linear Algebra of Curvature Tensors and Their Covariant Derivatives. Canadian journal of mathematics, Tome 40 (1988) no. 5, pp. 1105-1143. doi: 10.4153/CJM-1988-046-7
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