A normal field ν on a spacelike surface in R4 1 is called bi-normal if Kν, the determinant of the Weingarten map associated to ν, is zero. 
In this paper, we give a criterion to check if a normal field is bi-normal. Then we study the relationship between the spacelike pseudo-planar 
surfaces and spacelike pseudo-umbilical surfaces. We also study the bi-normal fields on spacelike ruled surfaces and spacelike surfaces of revolution.

Keywords: Lorentz–Minkowski space; spacelike surfaces; bi-normal fields; singularities of Gauss map; 
pseudo-planar surfaces; umbilicity.
AMS Subject Classification: 53C50, 53A35, 57R45

http://dx.doi.org/10.1142/S1793557116500522