Geodesic
How many are affine connections with torsion
Archivum mathematicum, Tome 50 (2014) no. 5, pp. 257-264 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The question how many real analytic affine connections exist locally on a smooth manifold $M$ of dimension $n$ is studied. The families of general affine connections with torsion and with skew-symmetric Ricci tensor, or symmetric Ricci tensor, respectively, are described in terms of the number of arbitrary functions of $n$ variables.
The question how many real analytic affine connections exist locally on a smooth manifold $M$ of dimension $n$ is studied. The families of general affine connections with torsion and with skew-symmetric Ricci tensor, or symmetric Ricci tensor, respectively, are described in terms of the number of arbitrary functions of $n$ variables.
DOI : 10.5817/AM2014-5-257
Classification : 35A10, 35F35, 35G50, 35Q99
Keywords: affine connection; Ricci tensor; Cauchy-Kowalevski Theorem 
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Dušek, Zdeněk; Kowalski, Oldřich. How many are affine connections with torsion. Archivum mathematicum, Tome 50 (2014) no. 5, pp. 257-264. doi: 10.5817/AM2014-5-257

[1] Arias-Marco, T., Kowalski, O.: Classification of locally homogeneous affine connections with arbitrary torsion on 2-dimensional manifolds. Monatsh. Math. 153 (2008), 1–18. | DOI | MR | Zbl

[2] Dušek, Z., Kowalski, O.: How many are torsion-less affine connections in general dimension. to appear in Adv. Geom.

[3] Egorov, Yu.V., Shubin, M.A.: Foundations of the Classical Theory of Partial Differential Equations. Springer-Verlag, Berlin, 1998. | MR | Zbl

[4] Eisenhart, L.P.: Fields of parallel vectors in a Riemannian geometry. Trans. Amer. Math. Soc. 27 (4) (1925), 563–573. | DOI | MR

[5] Helgason, S.: Differential Geometry, Lie Groups, and Symmetric Spaces. American Mathematical Soc., 1978. | MR | Zbl

[6] Kobayashi, S., Nomizu, N.: Foundations of differential geometry I. Wiley Classics Library, 1996.

[7] Kowalevsky, S.: Zur Theorie der partiellen Differentialgleichung. J. Reine Angew. Math. 80 (1875), 1–32.

[8] Kowalski, O., Sekizawa, M.: Diagonalization of three-dimensional pseudo-Riemannian metrics. J. Geom. Phys. 74 (2013), 251–255. | DOI | MR | Zbl

[9] Mikeš, J., Vanžurová, A., Hinterleitner, I.: Geodesic Mappings and some Generalizations. Palacky University, Olomouc, 2009. | MR

[10] Nomizu, K., Sasaki, T.: Affine Differential Geometry. Cambridge University Press, 1994. | MR | Zbl

[11] Petrovsky, I.G.: Lectures on Partial Differential Equations. Dover Publications, Inc., New York, 1991. | MR

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