How many are equiaffine connections with torsion
Zdeněk Dušek; Oldřich Kowalski
Archivum Mathematicum (2015)
- Volume: 051, Issue: 5, page 265-271
- ISSN: 0044-8753
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topDušek, Zdeněk, and Kowalski, Oldřich. "How many are equiaffine connections with torsion." Archivum Mathematicum 051.5 (2015): 265-271. <http://eudml.org/doc/276238>.
@article{Dušek2015,
abstract = {The question how many real analytic equiaffine connections with arbitrary torsion exist locally on a smooth manifold $M$ of dimension $n$ is studied. The families of general equiaffine connections and with skew-symmetric Ricci tensor, or with symmetric Ricci tensor, respectively, are described in terms of the number of arbitrary functions of $n$ variables.},
author = {Dušek, Zdeněk, Kowalski, Oldřich},
journal = {Archivum Mathematicum},
keywords = {affine connection; Ricci tensor; Cauchy-Kowalevski Theorem; affine connection; Ricci tensor; Cauchy-Kowalevski theorem},
language = {eng},
number = {5},
pages = {265-271},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {How many are equiaffine connections with torsion},
url = {http://eudml.org/doc/276238},
volume = {051},
year = {2015},
}
TY - JOUR
AU - Dušek, Zdeněk
AU - Kowalski, Oldřich
TI - How many are equiaffine connections with torsion
JO - Archivum Mathematicum
PY - 2015
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 051
IS - 5
SP - 265
EP - 271
AB - The question how many real analytic equiaffine connections with arbitrary torsion exist locally on a smooth manifold $M$ of dimension $n$ is studied. The families of general equiaffine connections and with skew-symmetric Ricci tensor, or with symmetric Ricci tensor, respectively, are described in terms of the number of arbitrary functions of $n$ variables.
LA - eng
KW - affine connection; Ricci tensor; Cauchy-Kowalevski Theorem; affine connection; Ricci tensor; Cauchy-Kowalevski theorem
UR - http://eudml.org/doc/276238
ER -
References
top- Dušek, Z., Kowalski, O., How many are torsion-less affine connections in general dimension, to appear in Adv. Geom.
- Dušek, Z., Kowalski, O., 10.5817/AM2014-5-257, Arch. Math. (Brno) 50 (2014), 257–264. (2014) Zbl1340.53021MR3303775DOI10.5817/AM2014-5-257
- Egorov, Yu.V., Shubin, M.A., Foundations of the Classical Theory of Partial Differential Equations, Springer-Verlag, Berlin, 1998. (1998) Zbl0895.35003MR1657445
- Eisenhart, L.P., 10.1090/S0002-9947-1925-1501329-4, Trans. Amer. Math. Soc. 27 (4) (1925), 563–573. (1925) MR1501329DOI10.1090/S0002-9947-1925-1501329-4
- Helgason, S., Differential Geometry, Lie Groups, and Symmetric Spaces, Amer. Math. Soc., 1978. (1978) Zbl0451.53038MR1834454
- Kobayashi, S., Nomizu, N., Foundations of differential geometry I, , Wiley Classics Library, 1996. (1996)
- Kowalevsky, S., Zur Theorie der partiellen Differentialgleichung, J. Reine Angew. Math. 80 (1875), 1–32. (1875)
- Kowalski, O., Sekizawa, M., 10.1016/j.geomphys.2013.08.010, J. Geom. Phys. 74 (2013), 251–255. (2013) Zbl1280.53020MR3118584DOI10.1016/j.geomphys.2013.08.010
- Mikeš, J., Vanžurová, A., Hinterleitner, I., Geodesic Mappings and some Generalizations, Palacky University, Olomouc, 2009. (2009) Zbl1222.53002MR2682926
- Nomizu, K., Sasaki, T., Affine Differential Geometry, Cambridge University Press, 1994. (1994) Zbl0834.53002MR1311248
- Petrovsky, I.G., Lectures on Partial Differential Equations, Dover Publications, Inc., New York, 1991. (1991) MR1160355
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