On surfaces in the 3-dimensional Lorentz-Minkowski space

Angel Ferrandez and Pascual Lucas

Vol. 152 (1992), No. 1, 93–100

DOI: 10.2140/pjm.1992.152.93

Abstract

Let M_s² be a surface in the 3-dimensional Lorentz-Minkowski space 𝕃³ and denote by H its mean curvature vector field. This paper locally classifies those surfaces verifying the condition ΔH = λH, where λ is a real constant.

The classification is done by proving that M_s² has zero mean curvature everywhere or it is isoparametric, i.e., its shape operator has constant characteristic polynomial.

Mathematical Subject Classification 2000

Primary: 53A10

Secondary: 53C50

Milestones

Received: 10 August 1990

Revised: 12 October 1990

Published: 1 January 1992