Geodesic
Moduli space of symmetric connections
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part VII, Tome 292 (2002), pp. 22-39 
S. Dubrovskiy. Moduli space of symmetric connections. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part VII, Tome 292 (2002), pp. 22-39. http://geodesic.mathdoc.fr/item/ZNSL_2002_292_a2/
@article{ZNSL_2002_292_a2,
     author = {S. Dubrovskiy},
     title = {Moduli space of symmetric connections},
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     year = {2002},
     volume = {292},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_292_a2/}
}
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The action of origin-preserving diffeomorphisms on a space of jets of symmetric connections is considered. Dimensions of moduli spaces of generic connections are calculated. Poincaré series of the geometric structure of connection is constructed, and shown to be a rational function.