Extended cross product in a 3-dimensional almost contact metric manifold with applications to curve theory

In this work, we define a new cross product in 3-dimensional almost contact metric manifold and we study the theory of curves using this new cross product in this manifold. Besides, in the works of Baikousis, Blair [1] and Cho et al. [4], we observe that some theorems are incomplete and excessively generalized are thus their alternative proofs presented.