The bi-normal fields on spacelike surfaces in ℝ14

Abstract

A normal field [Formula: see text] on a spacelike surface in [Formula: see text] is called bi-normal if [Formula: see text], the determinant of the Weingarten map associated to [Formula: see text], 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.