On geometry of focal surfaces due to B-Darboux and type-2 Bishop frames in Euclidean 3-space

In Euclidean 3-space ${\mathrm{E}}^3$, a canonical subject is the focal surface of such a cliched space curve, which would be a two-dimensional corrosive with Lagrangian discontinuities. The tubular surfaces with respect to the B-Darboux frame and type-2 Bishop frame in ${\mathrm{E}}^3$ are given. These tubular surfaces' focal surfaces are then defined. For such types of surfaces, we acquire some results becoming Weingarten, flat, linear Weingarten conditions and we demonstrate that in ${\mathrm{E}}^3$, a tubular surface has no minimal focal surface. We also provide some examples of these types of surfaces.