If we rotate a two-sphere in R^3 so it stays centered about the origin then two points don't move.(adsbygoogle = window.adsbygoogle || []).push({});

If we rotate a three-sphere in R^4 while it stays centered about the origin can it be done so that all points move?

Does this have anything to do with the fact the S^3 is parallelizable while S^2 is not?

Thanks for any help!

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# Rotate a three-sphere so every point moves in R^4?

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