The Bi-normal fields on spacelike surfaces in $\mathbb R_1^4$

Abstract

A normal field on a spacelike surface in $R^4_1$ is called bi-normal if $K^{\nu}$, the determinant of Weingarten map associated with $\nu$, is zero. In this paper we give a relationship between the spacelike pseudo-planar surfaces and spacelike pseudo-umbilical surfaces, then study the bi-normal fields on spacelike ruled surfaces and spacelike surfaces of revolution.