Spacelike S-Willmore spheres in Lorentzian space forms

Abstract

We show that spacelike S-Willmore surfaces are the only spacelike Willmore surfaces with a duality in Lorentzian space forms. We obtain a classification of S-Willmore spheres in Lorentzian conformal space forms. Such a sphere must be congruent to either a complete spacelike stationary (H = 0) surface in R n 1 ; a super-Willmore sphere in S 2m+2 ; or a polar transform of a (j―1)― isotropic complete spacelike stationary (H = 0) surface in R 2j+2 1 . We also show that all Willmore spheres in Q 4 1 are conformal to a complete spacelike stationary surface in R 4 1 .