Abstract:
The class of surfaces that have a certain property (called complexnormal) in the five-dimensional sphere in $\mathbb C^3$ is considered. It is shown that the minimal tori in this class are described by the equation $u_{z\overline{z}}=e^{-2u}-e^u$, which can be integrated by the inverse scattering method. The construction of finite-gap minimal tori that are complexnormal in the five-dimensional sphere in $\mathbb C^3$ is described.
Citation:
R. A. Sharipov, “Minimal tori in the five-dimensional sphere in $\mathbb C^3$”, TMF, 87:1 (1991), 48–56; Theoret. and Math. Phys., 87:1 (1991), 363–369
\Bibitem{Sha91}
\by R.~A.~Sharipov
\paper Minimal tori in the five-dimensional sphere in $\mathbb C^3$
\jour TMF
\yr 1991
\vol 87
\issue 1
\pages 48--56
\mathnet{http://mi.mathnet.ru/tmf5468}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1122779}
\zmath{https://zbmath.org/?q=an:0742.53021}
\transl
\jour Theoret. and Math. Phys.
\yr 1991
\vol 87
\issue 1
\pages 363--369
\crossref{https://doi.org/10.1007/BF01016575}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1991HG83500005}
Linking options:
https://www.mathnet.ru/eng/tmf5468
https://www.mathnet.ru/eng/tmf/v87/i1/p48
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