# How many are affine connections with torsion

## Zdeněk Dušek and Oldřich Kowalski

Address:

Zdeněk Dušek, University of Hradec Králové, Faculty of Science, Rokitanského 62, 500 03 Hradec Králové, Czech Republic and University of Ostrava, Faculty of Science, 30. dubna 22, 701 03 Ostrava, Czech Republic

Oldřich Kowalski, Charles University, Faculty of Mathematics and Physics, Sokolovská 83, 186 75 Praha 8, Czech Republic

E-mail:

zdenek.dusek@uhk.cz

kowalski@mff.cuni.cz

Abstract: 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.

AMSclassification: primary 35A10; secondary 35F35, 35G50, 35Q99.

Keywords: affine connection, Ricci tensor, Cauchy-Kowalevski Theorem.

DOI: 10.5817/AM2014-5-257