Surfaces in the 3-dimensional Lorentz-Minkowski space satisfying Δx = Ax + B

Luis Alías, Angel Ferrandez and Pascual Lucas

Vol. 156 (1992), No. 2, 201–208

DOI: 10.2140/pjm.1992.156.201

Abstract

In this paper we locally classify the surfaces M_s² in the 3-dimensional Lorentz-Minkowski space 𝕃³ verifying the equation Δx = Ax + B, where A is an endomorphism of 𝕃³ and B is a constant vector.

We obtain that classification by proving that M_s² has constant mean curvature and in a second step we deduce M_s² is isoparametric.

Mathematical Subject Classification 2000

Primary: 53C50

Secondary: 53C42

Milestones

Received: 30 April 1991

Published: 1 December 1992