SPACELIKE S-WILLMORE SPHERES IN LORENTZIAN SPACE FORMS

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) over right arrow = 0) surface in R-1(n); a super-Willmore sphere in S2m+2; or a polar transform of a (j - 1)-isotropic complete spacelike stationary ((H) over right arrow - 0) surface in R-1(2j+2). We also show that all Willmore spheres in Q(1)(4) are conformal to a complete spacelike stationary surface in R-1(4).