In this work, the directional spherical indicatrices of a timelike space curve using tangent, quasi-normal and quasi-binormal vectors with q-frame are introduced. Then we work on the condition, that a timelike space curve to be slant helix, by using the geodesic curvature of the directional normal spherical indicatrix. Finally, an application of the results is given.
In this paper, harmonic evolute surface of quasi binormal surface associated with quasi frame is studied. After constructing quasi binormal surface, we determine harmonic evolute surface of quasi binormal surface by using first and second fundamental forms. We then obtain some new results about these new surfaces and give some applications for them.
In this study, the ruled surfaces obtained by normal and binormal vectors along a timelike space curve by using q-frame are investigated in 3 dimensional Minkowski space. Directional evolutions of both quasi normal and quasi binormal ruled surfaces are studied by using their directrices. Then, we work on some geometric properties such as inextensibilty, developability and minimality of these ruled surfaces.
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