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We introduce a new type of slant curves in almost contact B-metric manifolds,called $\varphi $-slant curves, by an additional condition which is specificfor these manifolds. In this paper we study $\varphi $-slant null curves in aclass of 3-dimensional normal almost contact B-metric manifolds and prove thatfor non-geodesic of them there exists a unique Frenet frame for which theoriginal parameter is distinguished. We investigate some of $\varphi $-slantnull curves and with respect to the associated B-metric on the manifold andfind relationships between the corresponding Frenet frames and curvatures. Weconstruct the examined curves in a 3-dimensional Lie group and give theirmatrix representation.

Null $\varphi $-Slant Curves in a Main Class of 3-Dimensional Normal Almost Contact B-Metric Manifolds