I need to figure out the definition of the oft-called "Standard" action of the circle ##S^1 ## ( as a Topological/Lie group) ,on ##S^n##, the n-sphere ( I guess seen as ##\{z : |z|=1\}## in Euclidean n-space). My searches returned an action of ##S^1## on ##S^3 ## given by ##A(z_1, z_2): z --> (zz_1, zz_2) ## and ##z-->(zz_1, z^z_2)## , for z^ the conjugate of z, but no general definition for the action of ##S^1 ## on all ## S^n ##.