A Geometric Approach to Timelike Flows in Terms of Anholonomic
AbstractThis paper is devoted to the geometry of vector fields and timelike
flows in terms of anholonomic coordinates in three dimensional
Lorentzian space. We discuss eight parameters which are related by three
partial differential equations. Then, it is seen that the curl of
tangent vector field does not include any component in the direction of
principal normal vector field. This implies the existence of a surface
which contains both s-lines and b-lines. Moreover, we examine a normal
congruence of timelike surfaces containing the s-lines and b-lines .
Considering the compatibility conditions, we obtain the
Gauss-Mainardi-Codazzi equations for this normal congruence of timelike
surfaces in the case of the abnormality of normal vector field is zero.
Intrinsic geometric properties of this normal congruence of timelike
surfaces are obtained. We have deal with important results on these