Tubular surface generated by a curve lying on a regular surface and its characterizations

In this research, we have constructed and studied special tubular surfaces in Euclidean 3-space ${\mathbb{R}}^3$. We examined the singularities and geometrical properties of these surfaces. We achieved some significant results for these surfaces via Darboux frame. Also, we have proposed a few geometric invariants that illustrate the geometric characteristics of these surfaces, such as tubular Weingarten surfaces, using the traditional methods of differential geometry. Additionally, taking advantage of the singularity theory, we have given the classification of generic singularities of these surfaces. At last, we have presented some computational examples as an instance of use to validate our theoretical findings.