@article{AL-Dayel2022, 
author = {Ibrahim AL-Dayel and Emad Solouma and Meraj Khan},
title = {On geometry of focal surfaces due to B-Darboux and type-2 Bishop frames in Euclidean 3-space},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {7},
pages = {13454-13468},
keywords = {Euclidean geometry, focal surface, type-2 Bishop frame, tubular surface, B-Darboux frame},
url = {https://www.sciopen.com/article/10.3934/math.2022744},
doi = {10.3934/math.2022744},
abstract = {In Euclidean 3-space                      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                      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                      E              3  , a tubular surface has no minimal focal surface. We also provide some examples of these types of surfaces.}
}