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Symmetric connections, corrected version
*November 9, 2009*

*Posted by Akhil Mathew in differential geometry, MaBloWriMo.*

Tags: connections, corrections, symmetric connections, torsion tensor

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Tags: connections, corrections, symmetric connections, torsion tensor

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My post yesterday on the torsion tensor and symmetry had a serious error. For some reason I thought that connections can be pulled back. I am correcting the latter part of that post (where I used that erroneous claim) here. I decided not to repeat the (as far as I know) correct earlier part.

Proposition 1Let be a surface in , and let be a symmetric connection on . Then (more…)

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The torsion tensor and symmetric connections
*November 8, 2009*

*Posted by Akhil Mathew in differential geometry, MaBloWriMo.*

Tags: connections, symmetric connections, torsion tensor

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Tags: connections, symmetric connections, torsion tensor

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Today I will discuss the torsion tensor of a Koszul connection. It measures the deviation from being symmetric in a sense defined below.

**Torsion **

Given a Koszul connection on the smooth manifold , define the **torsion tensor** by