Im sorry to bother you, but im trying to understand one thing about embedding. Consider you have sphere embedded in the R^3, so you have a flat metrik. Otherwise you could describe the same sphere without embedding but with an induced metric.(adsbygoogle = window.adsbygoogle || []).push({});

My problem is to make clear that the Lie-Brackets of two tangentvectors in R^3 on the sphere are equal to the equivalent tangentvectors according to the induced metric.

( [X,Y]=[X',Y'] with g(X,Y)=g_induced(X',Y'))

thanks

by the way i think intuitionally it works...

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# Connection between Lie-Brackets an Embeddings

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