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I know that through the Maurer Cartan form on Lie Groups it's possible to define a Cartan connection. Let us suppose to restrict ourself to Matrix groups.

Is the Cartan connection originated by the Maurer Cartan form the same as the Levi-Civita connection? If not when they do coincide?

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  • $\begingroup$ What do you mean by the Levi-Civita connection? $\endgroup$ – Ted Shifrin Sep 10 '16 at 23:34
  • $\begingroup$ And what do you mean by a Cartan connection? You might be interested in this MathOverflow post. $\endgroup$ – Ted Shifrin Sep 10 '16 at 23:40
  • $\begingroup$ For Cartan connection I simply mean a connection defined by 1-forms, as results through the Maurer-Cartan form $\endgroup$ – Dac0 Sep 11 '16 at 10:21

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