A natural definition for convexity of space curves is given by requiring that the curve lies on the boundary of its convex hull. In this sense, the curves that you are describing will be convex.

Convex space curves have been well studied and have a number of interesting properties. For instance, when they are smooth, their torsion must vanish at least four times, which is a theorem of Sedykh. See this paper for a generalization of this result and other references in this area.

A natural definition for convex space curves is given by requiring that the curve lies on the boundary of its convex hull. In this sense, the curves that you describe will be convex.

Convex space curves have been well studied and have a number of interesting properties. For instance, when they are smooth, their torsion must vanish at least four times, which is a theorem of Sedykh. See this paper for a recent generalization of this result based on Arnold's tennis balls theorem, and other references in this area.