Related papers: Geodesics and isometric immersions in kirigami

Surfaces of finite geometric type are complete, immersed into the tree-dimensional Euclidean space with finite total curvature and Gauss map extending to an oriented compact surface as a smooth branched covering map over the unit sphere of…

Non-Euclidean surfaces are ubiquitous in numerous engineering fields, such as automotive, aerospace, and biomedical engineering domains. Morphing origami has numerous potential engineering applications, including soft robots, mechanical…

We study the geodesic motion planning problem for complete Riemannian manifolds and investigate their geodesic complexity, an integer-valued isometry invariant introduced by D. Recio-Mitter. Using methods from Riemannian geometry, we…

We derive the exact generating function for planar maps (genus zero fatgraphs) with vertices of arbitrary even valence and with two marked points at a fixed geodesic distance. This is done in a purely combinatorial way based on a bijection…

We prove that the pleated hyperbolic paraboloid, a familiar origami model known since 1927, in fact cannot be folded with the standard crease pattern in the standard mathematical model of zero-thickness paper. In contrast, we show that the…

Kirigami is an increasingly useful fabrication method to produce shape-programmable metamaterial structures. However, inverse design remains difficult because deployment is nonlinear, and feasible cut layouts must satisfy discrete…

Origami-inspired mechanisms can transform flat sheets into functional three-dimensional dynamic structures that are lightweight, compact, and capable of complex motion. These properties make origami increasingly valuable in robotic and…

Fully soft bistable mechanisms have shown extensive applications ranging from soft robotics, wearable devices, and medical tools, to energy harvesting. However, the lack of design and fabrication methods that are easy and potentially…

Miura-Ori, a celebrated origami pattern that facilitates functionality in matter, has found multiple applications in the field of mechanical metamaterials. Modifications of Miura-Ori pattern can produce curved configurations during folding,…

This article explores the limits of geometric construction using various tools, both classical and modern. Starting with ruler and compass constructions, we examine how adding methods such as origami, marked rulers (neusis), conic sections,…

We study geodesic motion in expanding spherical impulsive gravitational waves propagating in a Minkowski background. Employing the continuous form of the metric we find and examine a large family of geometrically preferred geodesics. For…

Let $V$ be a separable Hilbert space, possibly infinite dimensional. Let $\St(p,V)$ be the Stiefel manifold of orthonormal frames of $p$ vectors in $V$, and let $\Gr(p,V)$ be the Grassmann manifold of $p$ dimensional subspaces of $V$. We…

We investigate the geodesics in the entire class of nonexpanding impulsive gravitational waves propagating in an (anti-)de Sitter universe using the distributional form of the metric. Employing a 5-dimensional embedding formalism and a…

Experiments [1] have shown that auto-kirigami structures can grow on the surface of graphene because the graphene-graphene adhesion energy is greater than the graphene-substrate interaction. In this work molecular dynamics (MD) simulations…

This paper studies a specific metric on plane curves that has the property of being isometric to classical manifold (sphere, complex projective, Stiefel, Grassmann) modulo change of parametrization, each of these classical manifolds being…

In this paper we study singular riemannian foliations that have sections,i.e., totally geodesic complete immersed submanifolds that meet each leaf orthogonally and whose dimensions are the codimensions of the regular leaves. We prove here…

The space $J^k$ of $k$-jets of a real function of one real variable $x$ admits the structure of Carnot group type. As such, $J^k$ admits a submetry (\sR submersion) onto the Euclidean plane. Horizontal lifts of Euclidean lines (which are…

There are several ways of a construction of a boundary of a symmetric space using pencils of geodesics: the Karpelevich boundary, the visibility boundary, the associahedral boundary, and the sea urchin. We give explicit descriptions of…

Using an interface inserted in a background mesh is an alternative way of constructing a complex geometrical shape with a relative low meshing efforts. However, this process may require special treatment of elements cut by the interface.…

We develop a framework for characterizing isometric immersions of simply connected, bounded, planar regions with piecewise smooth boundaries into three-dimensional space. Each immersion is associated with a framed curve along the boundary…