Surfaces With Vanishing Abnormality of Normal Direction in Minkowski Space

Abstract

This paper is investigated geometry of vector fields along spacelike curve with timelike normal vector by using anholonomic coordinates. Derivative formulas of Frenet Serret frame of the curve are stated which includes eight parameters. Surfaces with vanishing abnormality of normal direction in Minkowski space are examined. Intrinsic geometric properties of these spacelike surfaces are investigated. Finally, the relations between spacelike surfaces with vanishing abnormality of normal direction and NLS, Heisenberg spin equation are investigated as applications.