We prove existence results
that give information about the space of minimal immersions of 2-tori into S3. More
specifically, we show:
For every positive integer n, there are countably many real n-dimensional
families of minimally immersed 2-tori in S3. Every linearly full minimal
immersion T2→ S3 belongs to exactly one of these families.
Let 𝒜 be the space of rectangular 2-tori. There is a countable dense subset
ℬ of 𝒜 such that every torus in ℬ can be minimally immersed into S3.
Mainly, we find minimal immersions that satisfy periodicity conditions and hence obtain
maps of tori, rather than simply immersions of the plane. This work uses a
correspondence, established by Hitchin, between minimal tori in S3 and algebraic
curve data.
