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arXiv · 2404.16788

Rectifying submanifolds of Riemannian manifolds with anti-torqued axis

Muhittin Evren Aydin·Adela Mihai·Cihan Özgür
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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.

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Muhittin Evren Aydin, Adela Mihai, Cihan Özgür. 2024-04-25. Rectifying submanifolds of Riemannian manifolds with anti-torqued axis. https://arxiv.org/abs/2404.16788

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