Minimal surfaces in the three-dimensional sphere with high symmetry
Keyword(s):
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.
Keyword(s):
2021 ◽
Vol 61
(1)
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1990 ◽
Vol 108
(4)
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pp. 989-989
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2020 ◽
Vol 23
(3)
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pp. 306-311
2012 ◽
Vol 62
(9)
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pp. 1903-1914
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2014 ◽
Vol 195
(1)
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pp. 95-110
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