On Differential Analysis of Flows on Normal Congruence of Spacelike Surfaces

Abstract

The present paper examines the differential analysis of fows on normal congruence of spacelike surfaces with spacelike normal vector in terms of anholonomic coordinates in three dimensional Lorentzian space. Eight parameters which are related by three partial differential equations are discussed. Then, it is seen that the curl of tangent vector field does not include any component with principal normal direction. Thus there exists a surface which contains both s-lines and b-lines. Also, we examine a normal congruence of spacelike surfaces containing the s-lines and b-lines. By compatibility conditions, Gauss-Mainardi-Codazzi equations for this normal congruence of spacelike surface are obtained: Intrinsic geometric properties of this normal congruence of spacelike surfaces are given.