In this paper, we recall some general properties and theorems about Translating Solitons in Semi Riemannian Manifolds. Moreover, we investigate those which are invariant by the action of a Lie group of isometries of the ambient space, by paying attention to the behaviour close to the singular orbit (if any) and at infinity. Then, we provide some related examples.
A basic goal of this paper is to investigate the tubular surface constructed by the spherical indicatrices of any spatial curve in the Euclidean 3− space. This kind of tubular surface is designed for the alternative moving frame {N, C, W } in conjunction with finding a relationship between the tubular surfaces and their special curves, such as geodesic curves, asymptotic curves, and minimal curves. The minimal curve γ on a surface is defined by the property that its fundamental coefficients satisfy Eq. (3.7) along the curve γ . At the end of this article, we exemplify these curves on the tubular surfaces with their figures using the program Mathematica.
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