Spacelike S-Willmore spheres in Lorentzian space forms

Peng Wang

Vol. 246 (2010), No. 2, 495–510

DOI: 10.2140/pjm.2010.246.495

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 R₁ⁿ; a super-Willmore sphere in S^2m+2; or a polar transform of a (j − 1)-isotropic complete spacelike stationary (H = 0) surface in R₁^2j+2. We also show that all Willmore spheres in Q₁⁴ are conformal to a complete spacelike stationary surface in R₁⁴.

Keywords

spacelike S-Willmore surfaces, spacelike S-Willmore sphere, stationary surfaces, duality theorem

Mathematical Subject Classification 2000

Primary: 53A30

Secondary: 53B30

Milestones

Received: 15 May 2009

Revised: 5 September 2009

Accepted: 6 October 2009

Published: 1 June 2010