Timelike Surfaces of Constant Mean Curvature in Minkowski 3-Space

Timelike Constant Mean Curvature Surfaces with Singularities

We use integrable systems techniques to study the singularities of timelike non-minimal constant mean curvature (CMC) surfaces in the LorentzMinkowski 3-space. The singularities arise at the boundary of the Birkhoff big cell of the loop group involved. We examine the behaviour of the surfaces at the big cell boundary, generalize the definition of CMC surfaces to include those with finite, gener...

Constant Mean Curvature Surfaces in Euclidean and Minkowski 3-spaces

Spacelike constant mean curvature surfaces in Minkowski 3-space L have an infinite dimensional generalized Weierstrass representation. This is analogous to that given by Dorfmeister, Pedit and Wu for constant mean curvature surfaces in Euclidean space, replacing the group SU(2) with SU(1, 1). The non-compactness of the latter group, however, means that the Iwasawa decomposition of the loop grou...

Weierstrass Representation for Timelike Minimal Surfaces in Minkowski 3-space

Using techniques of integrable systems, we study a Weierstraß representation formula for timelike surfaces with prescribed mean curvature in Minkowski 3-space. It is shown that timelike minimal surfaces are obtained by integrating a pair of Lorentz holomorphic and Lorentz antiholomorphic null curves in Minkowski 3-space. The relationship between timelike minimal surfaces and bosonic Nambu-Goto ...

Timelike Surfaces of Constant Mean Curvature ±1 in Anti-de Sitter 3-space H 3 1 (−1)

It is shown that timelike surfaces of constant mean curvature ±1 in anti-de Sitter 3-space H 1 (−1) can be constructed from a pair of Lorentz holomorphic and Lorentz antiholomorphic null curves in PSL2R via Bryant type representation formulae. These Bryant type representation formulae are used to investigate an explicit one-to-one correspondence, the so-called Lawson-Guichard correspondence, be...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form