Bicomplex extensions of zero mean curvature surfaces in R2,1 and R2,2

Abstract

Abstract In this paper, we construct zero mean curvature complex surfaces in C N with a various type of standard metric, each of which changes its type from positive definite to neutral, by means of bicomplex numbers. By applying them as bicomplex extensions, we describe the correspondence between fold singularities and type-changing of zero mean curvature real surfaces in R 2 , 1 and R 2 , 2 . In particular, we show that any fold singularity consists of branch points of the bicomplex extension. We also show that type-changing across a lightlike line segment occurs on an incomplete end on a fold singularity.