arXiv research

The paper studies timelike loxodromes on specific Lorentzian helicoidal surfaces.

Study spacelike loxodromes on helicoidal surfaces in Lorentzian n-space.

The study characterizes loxodromes on specific rotational surfaces in 3D space.

In this paper, we prove important results concerning the loxodromes on an invariant surface in a three-dimensional Riemannian manifold, some of which generalize classical results about loxodromes on rotational surfaces in $\mathbb{R}^3$. In particular, we show how to parametrize a loxodrome on an invariant surface of $…

The paper studies loxodromes on twisted surfaces in a specific 3D space.

Characterizes loxodromic unit vector fields on punctured spheres.

Loxodromic elements are pseudo-Anosov on specific graphs.

Study loxodromes and geodesics on rotational surfaces in pseudo-isotropic space.

New group with non-loxodromic Morse element found.

Generates special homeomorphisms for complex surfaces.

New loxodromic elements found in infinite-type surfaces.

Study of loxodromes on twisted surfaces in 3D space.

Curved loxodromes on spheres are explained and their ODE derived.

Flow on curves in inversive geometry converges to loxodromics.

The class of acylindrically hyperbolic groups, which are groups that admit a certain type of non-elementary action on a hyperbolic space, contains many interesting groups such as non-exceptional mapping class groups and $\operatorname{Out}(\mathbb F_n)$ for $n\geq 2$. In such a group, a generalized loxodromic element i…

Let ${\bf H}_{\mathbb C}^n$ be the $n$-dimensional complex hyperbolic space and ${\rm SU}(n,1)$ be the (holomorphic) isometry group. An element $g$ in ${\rm SU}(n,1)$ is called loxodromic or hyperbolic if it has exactly two fixed points on the boundary $\partial {\bf H}_{\mathbb C}^n$. We classify ${\rm SU}(n,1)$ conju…

The study examines groups acting loxodromically on hyperbolic graph products.

Artin-Tits groups act on a certain delta-hyperbolic complex, called the "additional length complex". For an element of the group, acting loxodromically on this complex is a property analogous to the property of being pseudo-Anosov for elements of mapping class groups. By analogy with a well-known conjecture about mappi…

In this paper, we obtain the differential equations of the space-like loxodromes on the non-degenerate canal surfaces depending on the causal characters of these canal surfaces and their meridians in Minkowski 3-space. Also we give an example by using Mathematica computer programme.

In this paper we prove that a fully irreducible outer automorphism relative to a non-exceptional free factor system acts loxodromically on the relative free factor complex as defined by Handel and Mosher. We also prove a north-south dynamic result for the action of such outer automorphisms on the closure of relative ou…

We construct an example of an isometric action of $F(a,b)$ on a $δ$-hyperbolic graph $Y$, such that this action is acylindrical, purely loxodromic, has asymptotic translation lengths of nontrivial elements of $F(a,b)$ separated away from $0$, has quasiconvex orbits in $Y$, but such that the orbit map $F(a,b)\to Y$ is n…

The paper counts conjugacy classes of loxodromic elements in Anosov subgroups with a power saving error term.

New infinite-type loxodromic elements found in surface mapping classes.

The paper proves inequalities for isometries in loxodromic Kleinian groups.

Let $G \curvearrowright X$ be a nonelementary action by isometries of a hyperbolic group $G$ on a hyperbolic metric space $X$. We show that the set of elements of $G$ which act as loxodromic isometries of $X$ is generic. That is, for any finite generating set of $G$, the proportion of $X$--loxodromics in the ball of ra…

Shifts are not type-preserving on surface graphs.

Study on complex hyperbolic bidisk isometries and their Dirichlet domains.

Study of timelike surfaces in Minkowski space with specific geometric properties.

Let $ξ$ and $η$ be two non--commuting isometries of the hyperbolic $3$--space $\mathbb{H}^3$ so that $Γ=\langleξ,η\rangle$ is a purely loxodromic free Kleinian group. For $γ\inΓ$ and $z\in\mathbb{H}^3$, let $d_γz$ denote the distance between $z$ and $γ\cdot z$. Let $z_1$ and $z_2$ be the mid-points of the shortest geod…

Extends Newton's minimal resistance problem to Riemannian surfaces.

In this paper, using the classifications of timelike and spacelike ruled surfaces, we study the Mannheim offsets of timelike ruled surfaces in Minkowski 3-space. Firstly, we define the Mannheim offsets of a timelike ruled surface by considering the Lorentzian casual character of the offset surface. We obtain that the M…

We prove that finitely generated purely loxodromic subgroups of a right-angled Artin group $A(Γ)$ fulfill equivalent conditions that parallel characterizations of convex cocompactness in mapping class groups $\text{Mod}(S)$. In particular, such subgroups are quasiconvex in $A(Γ)$. In addition, we identify a milder cond…

Paper classifies timelike Bonnet surfaces in Lorentzian 3-manifolds.

The study proves timelike Ricci bounds for low regularity spacetimes using optimal transport.

In this paper, we introduce the dual geodesic trihedron (dual Darboux frame) of a timelike ruled surface. By the aid of the E. Study Mapping, we consider timelike ruled surfaces as dual hyperbolic spherical curves and define the Mannheim offsets of timelike ruled surfaces by means of dual Darboux frame. We obtain the r…

In Garside groups, axes of Morse elements are strongly contracting.

Timelike curvature and Brunn-Minkowski inequality linked in non-smooth spacetimes.

This study examines geometric properties and offsets of slant timelike-ruled surfaces.

The study classifies timelike meridian surfaces in Minkowski 4-space.

Paper proves timelike minimal surfaces with any number of ends exist.

Timelike geometry of spherical simplices is shown to be isometric to vector spaces.

Timelike Thomsen surfaces are timelike minimal surfaces that are also affine minimal. In this paper, we make use of both the Lorentz conformal coordinates and the null coordinates, and their respective representation theorems of timelike minimal surfaces, to obtain a complete global classification of these surfaces and…

The paper proves properties of Lipschitz spacetimes with bounded Ricci curvature.

Timelike curves in Lorentzian length spaces have a total curvature notion that agrees with smooth curves.

New method finds closed timelike geodesics on Lorentzian manifolds.

We introduce a new approach to the study of timelike minimal surfaces in the Lorentz-Minkowski space through a split-complex representation formula for this kind of surface. As applications, we solve the Björling problem for timelike surfaces and obtain interesting examples and related results. Using the Björling repre…

Study timelike meridian surfaces in Minkowski 4-space with specific properties.

Study timelike minimal surfaces in Heisenberg group using harmonic maps.