A CHARACTERIZATION OF MAXIMAL SURFACES IN TERMS OF THE GEODESIC CURVATURES

Abstract

Maximal surfaces have a prominent place in the field ofdifferential geometry, captivating researchers with their intriguingproperties. Bearing a direct analogy to the minimal surfaces inEuclidean space, investigating both their similarities and differenceshas long been an important issue. This paper is aimed to give a localcharacterization of maximal surfaces in L3 in terms of their geodesiccurvatures, which is analogous to the minimal surface case presentedin [8]. We present a classification of the maximal surfaces undersome simple condition on the geodesic curvatures of the parametercurves in the line of curvature coordinates