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- Thread starter mertcan
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- #3

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I could not entirely conceive of the example you mentioned, could you please give some mathematical notations??

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I am not sure about the anti-symmetry bit, but so far as torsion is concerned, the torsion tensor will in general be non-zero if you choose a connection on your manifold which is not Levi-Civitá.

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Define the vector fields ##\partial_\theta## and ##(1/\sin\theta)\partial_\varphi## as parallel (this is sufficient to deduce the connection coefficients). The corresponding affine connection is not torsion free and corresponds to the situation described in my previous post.I could not entirely conceive of the example you mentioned, could you please give some mathematical notations??

It should be noted that the affine connection defind this way is metric compatible with the standard metric.

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haushofer

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http://math.stackexchange.com/quest...nian-manifolds-with-zero-curvature-and-nonzer

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