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...

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Connection between Lie-Brackets an Embeddings

**Physics Forums | Science Articles, Homework Help, Discussion**