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Why is the Lie Bracket the same as the Cross Product for a 2 Sphere in R3?
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[QUOTE="fresh_42, post: 6258149, member: 572553"] Any normal vector on a sphere is a tangent vector at a different spot. I'm not sure which Lie group is associated with the cross product, I assume ##SO(3)## fits best. But the sphere itself is two dimensional and corresponds to the quotient group ##SO(3)/SO(2)##. Maybe the ##3-##sphere ##SO(4)/SO(3)## works one-to-one. [/QUOTE]
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Why is the Lie Bracket the same as the Cross Product for a 2 Sphere in R3?
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