RECTIFYING SUBMANIFOLDS OF RIEMANNIAN MANIFOLDS WITH ANTI-TORQUED AXIS - Aydin, Muhittin evren; Mihai, Adela; Ozgur, Cihan (Korean Mathematical Soc, 2025)
In this paper we study rectifying submanifolds of a Riemannian manifold endowed with an anti-torqued vector field. For this, we first determine a necessary and sufficient condition for the ambient space to admit such a vector field. Then we characterize submanifolds for which an anti-torqued vector field is always assumed to be tangent or normal. A similar characterization is also done in the case of the torqued vector fields. Finally, we obtain that the rectifying submanifolds with anti-torqued axis are the warped products whose warping function is a first integration of the conformal scalar of the axis.
Keywords: Riemannian manifold; anti-torqued vector field; warped product; rectifying submanifold