ON ELLIPTIC LINEAR TIMELIKE PARALLEL WEINGARTEN SURFACES SATISFYING THE CONDITION 2a^rH^r + b^rK^r = c^r

Abstract

In this study, firstly, we obtain the parallel Weingarten surfaceswhich satisfy the condition 2aHr+ brKr= cin Minkowski 3-space. Thenwe give some geometric properties of these kind of surfaces, such as theirGauss map Nrand conformal structures. By using the conformal structuresinduced by arψr− brN, we derive two fundamental elliptic partial differentialequations which involve the immersion and the Gauss map