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

TL;DR

This paper investigates bi-normal fields on spacelike surfaces in four-dimensional Minkowski space, exploring their relationships with pseudo-planar and pseudo-umbilical surfaces, and analyzing specific cases like ruled surfaces and surfaces of revolution.

Contribution

It establishes relationships between pseudo-planar and pseudo-umbilical spacelike surfaces and studies bi-normal fields on ruled surfaces and surfaces of revolution in Minkowski space.

Findings

Relationship between pseudo-planar and pseudo-umbilical surfaces established

Characterization of bi-normal fields on ruled surfaces

Analysis of bi-normal fields on surfaces of revolution

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.