Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms

Abstract

Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms, a topic in Lorentzian conformal geometry which parallels the theory of Willmore surfaces in $S^4$, are studied in this paper. We define two kinds of transforms for such a surface, which produce the so-called left/right polar surfaces and the adjoint surfaces. These new surfaces are again conformal Willmore surfaces. For them holds interesting duality theorem. As an application spacelike Willmore 2-spheres are classified. Finally we construct a family of homogeneous spacelike Willmore tori.

19 pages

References in corpus (2)

• Adjoint Transform of Willmore Surfaces in $n$-sphere
• Polar transform of Spacelike isothermic surfaces in 4-dimensional Lorentzian space forms

Cited by in corpus (9)

• The Conformal Willmore Functional: a Perturbative Approach
• Willmore surfaces in spheres via loop groups $I$: generic cases and some examples
• Harmonic maps of finite uniton type into inner symmetric spaces
• Classification of Willmore 2-spheres in the 5-dimensional sphere
• Generalized polar transforms of spacelike isothermic surfaces
• Willmore surfaces in spheres via loop groups III: on minimal surfaces in space forms
• Global geometry and topology of spacelike stationary surfaces in the 4-dimensional Lorentz space
• Weierstrass-Kenmotsu representation of Willmore surfaces in spheres
• On Willmore surfaces in S^n of flat normal bundle