Abstract
Using the Lawson existence theorem of minimal surfaces and the symmetries of the Hopf fibration, we will construct symmetric embedded closed minimal surfaces in the three-dimensional sphere. These surfaces contain the Clifford torus, the Lawson’s minimal surfaces, and seven new minimal surfaces with genera [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. We will also discuss the relation between such surfaces and the maximal extendable group actions on subsurfaces of the three-dimensional sphere.
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