Rectifying submanifolds of Riemannian manifolds with anti-torqued axis

TL;DR

This paper investigates rectifying submanifolds within Riemannian manifolds equipped with anti-torqued vector fields, providing conditions for their existence and characterizations of their geometric properties.

Contribution

It introduces a necessary and sufficient condition for the ambient space to admit anti-torqued vector fields and characterizes submanifolds with such fields as warped products with specific warping functions.

Findings

Characterization of anti-torqued vector fields in Riemannian manifolds

Conditions for submanifolds with tangent or normal anti-torqued fields

Rectifying submanifolds as warped products with conformal scalar-based warping functions

Abstract

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.