Related papers: On curves with nonnegative torsion

This paper discusses the observed at rotation curves of galaxies in the context of noncommutative geometry. The energy density of such a geometry is diffused throughout a region due to the uncertainty encoded in the coordinate commutator.…

It was shown earlier by Rahaman et al. that a noncommutative-geometry background can account for galactic rotation curves without the need for dark matter. The smearing effect that characterizes noncommutative geometry is described by means…

In this paper, we give smoe characterizations of relatively normal-slant helices and isophotic curves on a smooth surface immersed in Euclidean 3-space with respect to their position vevtor. We also introduce the methods for generating an…

Steinerberger proposed a notion of curvature on graphs involving the graph distance matrix (J. Graph Theory, 2023). We show that nonnegative curvature is almost preserved under three graph operations. We characterize the distance matrix and…

In the round 6-sphere, null-torsion holomorphic curves are fundamental examples of minimal surfaces. This class of minimal surfaces is quite rich: By a theorem of Bryant, extended by Rowland, every closed Riemann surface may be conformally…

We study the global structure of Lorentzian manifolds with partial sectional curvature bounds. In particular, we prove completeness theorems for homogeneous and isotropic cosmologies as well as static spherically symmetric spacetimes. The…

We prove that a Riemannian submersion between smooth, compact, non-negatively curved Riemannian manifolds has to be smooth, resolving a conjecture by Berestovskii--Guijarro. We show that without any curvature assumption, the smoothness of…

Consider the Euclidean space $\mathbb{R}^3$ endowed with a canonical semi-symmetric non-metric connection determined by a vector field $\mathsf{C}\in\mathfrak{X}(\mathbb{R}^3)$. We study surfaces when the sectional curvature with respect to…

We present a novel, deterministic, and efficient method to detect whether a given rational space curve is symmetric. By using well-known differential invariants of space curves, namely the curvature and torsion, the method is significantly…

In this paper, we prove a general halfspace theorem for constant mean curvature surfaces. Under certain hypotheses, we prove that, in an ambient space M^3, any constant mean curvature H_0 surface on one side of a constant mean curvature H_0…

For a manifold with an affine connection, we prove formulas which infinitesimally quantify the gap in a certain naturally defined open geodesic quadrilateral associated to a pair of tangent vectors $u$, $v$ at a point of the manifold. We…

Paths in an appropriate geometry are usually used as trajectories of test particles in geometric theories of gravity. It is shown that non-symmetric geometries possess some interesting quantum features. Without carrying out any quantization…

Let $\mathbb{Q}_3$ be the complex 3-quadric endowed with its standard complex conformal structure. We study the complex conformal geometry of isotropic curves in $\mathbb{Q}_3$. By an isotropic curve we mean a nonconstant holomorphic map…

We show that if the curvature of a Cartan-Hadamard $n$-manifold is constant near a convex hypersurface $\Gamma$, then the total Gauss-Kronecker curvature $\mathcal{G}(\Gamma)$ is not less than that of any convex hypersurface nested inside…

On one hand, we study the class of graphs on surfaces, satisfying tessellation properties, with positive Forman curvature on each edge. Via medial graphs, we provide a new proof for the finiteness of the class, and give a complete…

Let $G$ be a simple topological graph and let $\Gamma$ be a polyline drawing of $G$. We say that $\Gamma$ \emph{partially preserves the topology} of $G$ if it has the same external boundary, the same rotation system, and the same set of…

We prove a compactness theorem for holomorphic curves in 4-dimensional symplectizations that have embedded projections to the underlying 3-manifold. It strengthens the cylindrical case of the SFT compactness theorem by using intersection…

We introduce the notion of conformal trajectories in three-dimensional Riemannian manifolds $M^3$. Given a conformal vector field $V\in\mathfrak{X}(M^3)$, a conformal trajectory of $V$ is a regular curve $\gamma$ in $M^3$ satisfying…

We consider the symmetric teleparallel $f\left( Q\right) $-gravity in Friedmann--Lema\^{\i}tre--Robertson--Walker cosmology with nonzero spatial curvature. For a nonlinear $f\left( Q\right) $ model there exist always the limit of General\…

We prove that closed manifolds admitting a generic metric whose sectional curvature is locally quasi-constant are graphs of space forms. In the more general setting of QC spaces where sets of isotropic points are arbitrary, under suitable…