Related papers: On a class of linearizable planar geodesic webs
We show a one-to-one correspondence between arrangements of d lines in the projective plane, and lines in P^{d-2}. We apply this correspondence to classify (3,q)-nets over the complex numbers for all q<=6. When q=6, we have twelve possible…
Geodesic nets on Riemannian manifolds form a natural class of stationary objects generalizing geodesics. Yet almost nothing is known about their classification or general properties even when the ambient Riemannian manifold is the Euclidean…
We classify totally geodesic submanifolds in Hopf-Berger spheres, which constitute a special family of homogeneous spaces diffeomorphic to spheres constructed via Hopf fibrations. As a byproduct of our investigations, we have discovered…
We construct a class of $3\otimes 3$ entangled edge states with positive partial transposes using indecomposable positive linear maps. This class contains several new types of entangled edge states with respect to the range dimensions of…
In this work, the Z$_3$-graded differential geometry of the quantum plane is constructed. The corresponding quantum Lie algebra and its Hopf algebra structure are obtained. The dual algebra, i.e. universal enveloping algebra of the quantum…
We show that a wide class of $W$-(super)algebras, including $W_N^{(N-1)}$, $U(N)$-superconformal as well as $W_N$ nonlinear algebras, can be linearized by embedding them as subalgebras into some {\em linear} (super)conformal algebras with…
Necessary and sufficient conditions for a sequence of positive integers to be the degree sequence of a 3-connected simple graph are detailed. Conditions are also given under which such a sequence is necessarily 3-connected i.e. the sequence…
In the present note we study combinatorial and algebraic properties of cubic-line arrangements in the complex projective plane admitting nodes, ordinary triple and $A_{5}$ singular points. We deliver a Hirzebruch-type inequality for such…
We present a complete classification of complex plane algebraic curves, equipped with the induced Euclidean, up to global bilipschitz homeomorphism.
A nonplanar graph G is called almost-planar if for every edge e of G, at least one of G\e and G/e is planar. In 1990, Gubser characterized 3-connected almost-planar graphs in his dissertation. However, his proof is so long that only a small…
In this paper, we give a new class of reconstructible graphs, which is an extension of my paper `A class of reconstructible graphs'.
We study straight-line drawings of planar graphs with few segments and few slopes. Optimal results are obtained for all trees. Tight bounds are obtained for outerplanar graphs, 2-trees, and planar 3-trees. We prove that every 3-connected…
The class of terminal planar networks was recently introduced from a biological perspective in relation to the visualization of phylogenetic networks, and its connection to upward planar networks has been established. We provide a…
We apply classical invariant theory of binary forms to explicitly characterize isomorphism classes of hyperelliptic curves of small genus and, conversely, propose algorithms for reconstructing hyperelliptic models from given invariants. We…
We give a combinatorial characterization of upward planar graphs in terms of upward planar orders, which are special linear extensions of edge posets.
This manuscript serves as an online supplement of a preprint, which presents a study on a kind of bilayer networks where some nodes (called interconnecting nodes) in two layers merge. A model showing an important general property of the…
This paper first gives a brief overview over some interesting descriptions of conic sections, showing formulations in the three geometric algebras of Euclidean spaces, projective spaces, and the conformal model of Euclidean space. Second…
We propose a simple method of explicit description of families of closed geodesics on a triaxial ellipsoid $Q$ that are cut out by algebraic surfaces in ${\mathbb R}^3$. Such geodesics are either connected components of spatial elliptic…
We consider the class F of 2-connected non-planar K_{3,3}-subdivision-free graphs that are embeddable in the projective plane. We show that these graphs admit a unique decomposition as a graph K_5 (the core) where the edges are replaced by…
We give a complete description of all order 1 invariants of planar curves.