The impact of intrinsic and extrinsic curvature on the distribution of topological defects (TDs) in neck‐like regions of biological membranes is studied quantitatively. Biological membranes are modeled effectively at the mesoscopic level as two‐dimensional films described in terms of the tensor nematic order parameter field and curvature fields. It is demonstrated that antidefects robustly form at the neck area and can promote a membrane fission. The assembling of antidefects near the catenoid's equatorial ring, where catenoids roughly mimic neck shapes are analyzed in more detail. It is demonstrated that for sufficiently strong curvatures, the effective topological charge Δmeff within a strongly curved region equals zero, and the resulting structures are topologically neutral. Consequently, the total charge of antidefects within the region equals Δm = −ΔmV − ΔmK. In most cases, the positions of antidefects are strongly influenced by the extrinsic curvature.