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Keywords:
affine connection; Ricci tensor; Cauchy-Kowalevski Theorem
affine connection; Ricci tensor; Cauchy-Kowalevski Theorem
Summary:
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.
References:
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