In this paper, we have a tendency to investigate a particular Weingarten and linear Weingarten varieties of canal surfaces according to Bishop frame in Euclidean 3-space E 3 satisfying some fascinating and necessary equations in terms of the Gaussian curvature, the mean curvature, and therefore the second Gaussian curvature. On the premise of those equations, some canal surfaces are introduced.

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In this paper we study three dimensional surfaces in  generated by equiform motions of a pseudohyperbolic surface. The properties of these surfaces up to the first order are investigated. We prove that three dimensional surfaces in  in general, is contained in a canal hypersurface, which is gained as envelope of a one-parametric set of 6-dimensional pseudohyperbolic. Finally we give an example.

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<abstract><p>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.</p></abstract>

Abstract:In this paper, the spacelike tubular surface with Darboux frame is introduced in Minkowski 3-space E 3 1 . Then, some characterizations were investigated for special curves on this tube with Darboux frame in Minkowski 3-space. Finally, we compute the Gaussian and mean curvature of tubular surface with Darboux frame.