Bonnet Canal Surfaces

We know that Bonnet surfaces are surfaces which can admit at least one non-trivial isometry that preserves the principal curvatures in the Euclidean three-dimensional space. In this study, firstly, we have examined in which conditions a particular type of swept surface named canal surfaces may be Bonnet surfaces. Secondly, we have defined Bonnet canal surfaces in the Euclidean three-dimensional space and have obtained some special results for the Bonnet canal surfaces. We have studied the Bonnet canal surfaces which will be formed when the curve generating the canal surface is a special curve. In addition, we have given an example for Bonnet canal surface by considering the obtained conditions