Isothermic and S-Willmore Surfaces as Solutions to Blaschke’s Problem
نویسنده
چکیده
Note that Blaschke and his school only considered surfaces in 3-space and ignored the higher co-dimension case. In Sn this problem is still meaningful. It is known that the construction of Darboux pair of isothermic surfaces as well as dual Willmore surfaces has a generalization to Sn (see [4, 9] and [7]), and they still constitute solutions to the generalized Blaschke’s problem. Here we will show they are exactly the only nontrivial solutions as before. In 3-space every Willmore surface is S-Willmore, so our theorem reduces to Blaschke’s result. The main theorem reads as follows:
منابع مشابه
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