arXiv subjects

Esra Dilmen

Publications and source records attributed to Esra Dilmen.

2 recordsLinked to original sources

arXiv2026

Prescribed Angle Surfaces Associated with Torse-Forming Vector Fields in Riemannian Manifolds

In this paper, we introduce the notion of a prescribed angle hypersurface in a Riemannian manifold associated with a pair $(\mathcal{V},\theta)$, where $\mathcal{V}$ is a unit vector field along the hypersurface and $\theta$ denotes the angle between $\mathcal{V}$ and the unit normal vector field of the hypersurface. We study such hypersurfaces in case $\mathcal{V}$ is a torse-forming vector field. In the particular $3$-dimensional case, we determine the intrinsic and extrinsic curvatures of these hypersurfaces in terms of the prescribed angle and the potential function of $\mathcal{V}$. Using this, we classify prescribed angle surfaces under suitable assumptions.

math.DG↗

arXiv2026

Curves in Riemannian Manifolds Making Prescribed Angles With Torse-Forming Vector Fields

In this paper, we introduce the notion of a prescribed angle curve in a Riemannian manifold associated with a pair $(\mathcal{V},\theta)$, where $\mathcal{V}$ is a unit vector field along the curve and $\theta$ denotes the angle between $\mathcal{V}$ and the principal normal vector of the curve. When $\mathcal{V}$ 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 $\mathcal{V}$. Moreover, using this notion, we provide a new characterization of curves lying on geodesic spheres in real space forms.

math.DG↗