Curves in Riemannian manifolds making prescribed angles with torse-forming vector fields

Abstract

In this paper, we introduce the notion of a prescribed angle curve in a Riemannian manifold associated with a pair (V, theta), where V is a unit vector field along the curve and theta denotes the angle between V and the principal normal vector of the curve. When V is a torse-forming vector field, we establish an existence result for prescribed angle curves. In the 3-dimensional case, we determine the curvatures of these curves in terms of the prescribed angle and the potential function of V. Moreover, using this notion, we provide a new characterization of curves lying on geodesic spheres in real space forms. (c) 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.