Abstract
In this study, a fundamental relation, as a base for the geometry of the time-like surfaces, among the Darboux vectors of an arbitrary time-like curve (c) on a time-like surface and the parameter curves (c1) and (c2) in the Minkowski 3-space R13 was founded.
Highlights
In this study, a fundamental relation, as a base for the geometry of the time-like surfaces, among the Darboux vectors of an arbitrary time-like curve (c) on a ti.me-like surface and the parameter curves (Cl) and in the Mmkowski 3space R~ was founded
For the unit vectors el, e2 e3 of the edges of a solid perpendicular trihedron that changes according to the real parameter t, the below formulae is valid: del dt where el and e2 are space-like vectors and e3 is a time-like vector and /\ is Lorentzian vectoral product [3]
Let any time-like curve that is passing through a point P on the surface be (c)
Summary
A fundamental relation, as a base for the geometry of the time-like surfaces, among the Darboux vectors of an arbitrary time-like curve (c) on a ti.me-like surface and the parameter curves (Cl) and (cz) in the Mmkowski 3space R~ was founded. Let us consider the time-like surface y = y(u, v). At every point of a time-like curve (c) on this surface there exists Frenet trihedron [t, n , b] . Let us show the curves' unit tangent vector as t and the surfaces' space-like normal unit vector as N at the point P on surface.
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